x/x-2 + x-1/x+1= -1
Can someone walk me through the steps of this problem? Much appreciated. :)
Answers
[tex]\large{\boxed{ \sf x = 1, \ x = 0 }[/tex]
Explanation:[tex]\sf \Rightarrow \dfrac{x}{x-2\:}+\:\dfrac{x-1}{x+1}=\:-1[/tex]
[tex]\sf \Rightarrow \dfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=\:-1[/tex]
[tex]\sf \Rightarrow \dfrac{x^2+x+x^2-2x-x + 2}{x^2 - 2x + x - 2}=\:-1[/tex]
[tex]\sf \Rightarrow 2x^2-2x+ 2=\:-1(x^2 - 2x + x - 2)[/tex]
[tex]\sf \Rightarrow 2x^2-2x+ 2=\:-x^2 + 2x - x + 2[/tex]
[tex]\sf \Rightarrow 2x^2+x^2 -2x - x+ 2-2=0[/tex]
[tex]\sf \Rightarrow 3x^2 - 3x = 0[/tex]
[tex]\sf \Rightarrow 3x(x - 1) = 0[/tex]
[tex]\sf \Rightarrow 3x = 0 , \ x - 1 = 0[/tex]
[tex]\sf \Rightarrow x = 0 , \ x =1[/tex]
Answer:
x = 0 or x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{x}{x-2}+\dfrac{x-1}{x+1}=-1[/tex]
Multiply the two denominators to get the same denominator:
Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.
Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.
[tex]\implies \dfrac{x(x+1)}{(x-2)(x+1)}+\dfrac{(x-2)(x-1)}{(x-2)(x+1)}=-1[/tex]
Add the numerators and keep the denominator so that there is now one fraction:
[tex]\implies \dfrac{x(x+1)+(x-2)(x-1)}{(x-2)(x+1)}=-1[/tex]
Simplify the numerator by expanding the brackets:
[tex]\implies \dfrac{x^2+x+x^2-3x+2}{(x-2)(x+1)}=-1[/tex]
[tex]\implies \dfrac{2x^2-2x+2}{(x-2)(x+1)}=-1[/tex]
Simplify the denominator by expanding the brackets:
[tex]\implies \dfrac{2x^2-2x+2}{x^2-x-2}=-1[/tex]
Multiply both sides by the denominator of the left side:
[tex]\implies 2x^2-2x+2=-1(x^2-x-2)[/tex]
Simplify and move everything to the left side:
[tex]\implies 2x^2-2x+2=-x^2+x+2[/tex]
[tex]\implies 3x^2-3x=0[/tex]
Factor:
[tex]\implies 3x(x-1)=0[/tex]
Therefore:
[tex]\implies 3x=0 \implies x=0[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
Therefore, x = 0 or x = 1
Related Questions
PLS ANSWER ASAP- THIS IS A 7th GRADE QUESTION AND IF UR ANSWER IS THE FIRST AND CORRECT, I WILL MARK BRAINLIEST
Answers
Answer:
x = 6
Explanation:
scale factor × original dimension = dilated dimension
inserting values:
0.25 × x = 1.5
0.25x = 1.5
x = 1.5/0.25
x = 6
The scale factor is the scale between two objects,
The scale factor is 0.25
1.5 divided by 0.25 equals 6
Therefore x equals 6
Lou's shoe was 9.178 inches long, Helen's shoe was 7.093 inches long, Jay's shoe was 10.554 inches long and Craig's shoe was 4.112 longer than Helen's. How long will the row of shoes be if someone placed them in a line from end to end?
Answers
Answer:
38.03 in
Step-by-step explanation:
Step 1: Calculate Craig's shoe length.
It's 4.112 in longer than Helen's shoe, which is 7.093 in. So, we simply add those two numbers to get 11.205.
Step 2: Add up all of the numbers
Now that we have everyone's shoe lengths, we just add them all up to get 38.03 in.
Hope this helps!
Answer:
38.03 in.
Step-by-step explanation:
38.03 in.
-34, -2 3/4, ____, -1.5, 0, 2.5, 10, 25 1/5
what number is missing
Answers
Answer:
c: -1 9/10
A: -2.5
B: -2
C: -1 9/10
D: -1
Please help me with this (i attached photos to cause less confusion)
Thanks :) 25 Points!!!
Answers
Answer:
See below
Step-by-step explanation:
The first two questions are slope = 0
a horizontal line has zero slope
slope = rise/run = 0 / run = 0
Greatest y value is + 4 from x = 3 to 4
the least y value is -3 fro x = -4 to -3
slope=rise/run=0
#1) and #2) both are slope=0
greatest y value is +4 from x=3 to 4.
then least y value is -3 from x=-4 to -3.
10 Points!!!
A cheese is in the shape of right prism with a triangular base and its dimensions are as shown. What is the approximate surface area of this prism?
A. 72 cm ²
B. 79.8 cm ²
C. 82 cm ²
D.87.4 cm ²
Answers
Answer:
79.8 cm²
Explanation:
surface area of triangular prism: (a + b + c) × length + base × height
Here given:
a = 3 cm, b = 3 cm, c = 3 cm, length = 8 cm, base = 3 cm, height = 2.6 cm
Inserting the values:
(a + b + c) × length + base × height
(3 + 3 + 3) × 8 + 3 × 2.6
79.8 cm²
More on surface area of triangular prism: https://brainly.com/question/27970162
Need HELP！！！！
Kirsten plans to dig a rectangular-shaped area in her yard for a garden.
She wants the garden to be 16 feet long and 10 feet wide.
1. Kirsten wants to sketch a scale drawing of the garden.
Part A
Draw and label the scale model. Use a scale of 1 inch equals 2.5 feet.
Part B
Kirsten considers enlarging the scale drawing by a scale factor of 4 to
include more details. What would be the new scale and dimensions of
the larger drawing?
2. Kirsten decides that one of the long edges of the garden will be adjacent
to the side of her house. She plans to put a 3-foot-high fence around the
other three sides. If she paints the fence on both sides, what is the total
area that will be painted? Explain.
Answers
Answer:
shortest length of fence is 8485.2 ft
Step-by-step explanation:
Given data
area = 3,000,000 square feet
to find out
shortest length of fence
let length L and width is W
so area is L × W
W = 3 × /L ............1
2W = 6 × /L
rectangular field and then divide it in half
so fencing will be 3 × L + 2 × W
i.e. 3 L + 2W
fencing = 3 L + 6 × /L
fencing minimum = 3 L - 6 × /L²
fencing minimum length will be zero
3 L - 6 × /L² = 0
3 L² = 6 ×
L² = 2 ×
L = 1414.2
so from equation 1
W = 3 × /L
W = 3 × /1414.2
W = 2121.3
so fencing will be 3 L +2 W
so fencing = 3 × 1414.2 +2 × 2121.3
fencing = 4242.6 +4242.6
fencing = 8485.2
shortest length of fence is 8485.2 ft
What was her mean score?
Answers
Answer:
154 is the mean
Step-by-step explanation:
First, you will add up all the numbers. This will give you a total of 770, then you have to divide the number, which is 5. So 770 ÷ 5 = 154.
I Hope This Helped :D
Answer:
154
Step-by-step explanation:
You can find the mean, or average, of a data set in two simple steps:
1. Find the sum of the values by adding them all up.
2. Divide the sum by the number of values in the data set.
Select ALL the correct answers.
The number of calls that the employees in a call center took on Wednesday were recorded and combined in the histogram below.
Which of the following statements describe the distribution?
The mean is the best measure of center.
The mean absolute deviation is the best measure of variability.
The interquartile range is the best measure of variability.
The data has one striking deviation.
The data is close together without any outliers.
The data is spread out with no gaps.
The median is the best measure of center.
Answers
Answer:
a-The mean is the best measure of center.
b-The mean absolute deviation is the best measure of variability.
c-The interquartile range is the best measure of variability.
g-The median is the best measure of center.
Step-by-step explanation:
a-The mean is the best measure of center.
b-The mean absolute deviation is the best measure of variability.
c-The interquartile range is the best measure of variability.
d-The data has one striking deviation.
e-The data is close together without any outliers.
f-The data is spread out with no gaps.
g-The median is the best measure of center.
Answer:
a-The mean is the best measure of center.
b-The mean absolute deviation is the best measure of variability.
c-The interquartile range is the best measure of variability.
g-The median is the best measure of center.
Step-by-step explanation:
HELP I WILL GIVE BRAINLIEST
Answers
Answer: There are 24 frames of animation in 1 second of anime.
Step-by-step explanation:
There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.
Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.
86400 ÷ 3600 = 24
There are 24 frames of animation in 1 second of anime.
the ratio of students who perfer coke to pepsi is 5 out of 7 if 84 students were serveyed how many students perfer pepsi
Answers
Answer:
24 students prefer pepsi to coke
Step-by-step explanation:
84 divided by 7 is 12
12 times five is 60
84 minus 60 results in 24 students
Answer:
It is 49 students.
Step-by-step explanation:
So, 5:7 in fraction form is 5/12 and 7/12 so when you you multiply 7/12 and 84 you get 48.72 and then you can round your answer to 49 students.
how much is 10 cents +6 dimes + 5 cents equal?
is it equal to a dollar?
Answers
Answer:
75 ¢
Step-by-step explanation:
10 cents +6 dimes + 5 cents equals 75 cents or 3/4 of a dollar
please help!!!!!!!!!!!!!!!!!!!!!!
Answers
the last option.
Hope this helped :)
graph y=4x-9
(just give me the coordinates)
Answers
Answer:
use desmos
Step-by-step explanation:
just type it in for easiest answer
Jenny has 36 cupcakes. How many kids (including Jenny) can share these cupcakes evenly?
The number of kids who can share 36 cupcakes evenly could be:
Answers
36/?
Smallest amount of kids per cupcake is 1
36/1
36 kids
i attached the question
Answers
Answer:
Step-by-step explanation:
Answer:
8.889%
Step-by-step explanation:
16/180 = 8.889 % First find area of cardboard then find larger area and then divide.
There are about 30.5 centimeters in a foot. There are 3 feet in a yard. About how many centimeters in a yard? Please explain how you got your answer
Answers
Because there is 30.5 centimeters in one foot, and 3 feet in a yard, you need to multiply 30.5 by 3 for each foot, or 30.5*3=91.5!
Answer:
[tex]10\frac{1}{6}[/tex]
HELP FAST!
Which of the following volume measurements is the best estimate for the
figure above? Round each measurement to the nearest whole number to get
your estimate
A. 324 in3
B. 216 in3
C. 360 in3
D. 300 in3
Answers
Answer:
c. 360 in^3
Step-by-step explanation:
1st you will want to round the decimals to the nearst whole number
2.7 is 3
and
9.8 is 10
2nd now that you rounded the decimal lengths you can multiply
12x3x10=360in^3
Ken had 5 math quizzes in a month.
Which table can be used to find his mean score on the quizzes?
Answers
Answer:
Choose the top right one.
Step-by-step explanation:
hoped i helped i really hope i helped. can you please please give me crown as well?
Your welcome:)
After we planted flowers in 2/5 of our garden, 24m squared remained unplanted. How many square meters is this garden in total?
(PLEASE ANSWER ASAP)
Answers
Answer:
60m²
Step-by-step explanation:
24 = 2/5
12 = 1/5
12 × 5 = 60
60 = 5/5
Answer:
60m^2
Step-by-step explanation:
I think
A box measures 1/4 ft. long, 1/6 ft. wide, and 1/3 ft. high. Find the volume of the
box in inches. Do not include units in your answer.
Answers
Steps:
1/4ft=3in
1/6ft=2in
1/3ft=4in
V=l*w^h
3(2)=6
6*4=24
The Answer is 24.
Answer this. Show your work. Worth 10 points. Under 4 hours. URGENT.
Answers
NO LINKS OR FILES PLEASE!!!!!!
Part B: Starting from the origin, explain how to plot the following three points accurately:
(1, −1)
(−1, 1.25)
(−2, fraction 3 over 4)
Answers
Answer:
refer to the above attachment !
Step-by-step explanation:
Mark as brainlest answer to This answer!
17. Find the perimeter of a circle that is 10cm in diameter.
3.1416 x 10 =
a)31.416cm
b) 31,156
c) 31,216
help plss
Answers
Step-by-step explanation:
I think the answer is (a) hope this helps
Explanation: calculated
Ryan has $100 to buy new clothes. If he buys 3 shirts that cost $29.23 each, including taxes,
how much money will he have left?
Answers
100 - 87.69 =$12.31
I’m not sure if you want to round it off
Or if you need to remove tax
but that’s what I got
Answer
$12.31
Step-by-step explanation:
29.23 x 3 = 87.69
100.00 - 87.69 = 12.31
pls answer 20 points I will mark brainliest
Answers
Answer:
So to find the volume of triangle prism,
Find area of triangle = [tex]\frac{1}{2} (5)(3)=\frac{15}{2} =7.5in^{2}[/tex]
Then find the total volume of triangle prism= 7.5×6=45in³
Volume of triangular prism = 45in³
Now to find the volume of the rectangular piece,
Volume=width×height×length
= 7×3×16
= 336 in³
Volume of rectangular piece = 336in³
Total area= 45in³+336in³=381in³
Please help 5 points each but beware if you use my points for no reason I'll report you
Answers
Answer:
v=⅓×6×9=18cm² hope it helps
Answer:
The answer is 18
Step-by-step explanation:
If the volume of a pyramid is 1/3 of the value base times height, and we have the measurements of the base and the height, then we fill in the equation like this:
1/3 [6 x 9] = volume
1/3 [54] = volume
18 = volume
The volume is 18
Lola started a swimming lesson at 1:30 p.m. that lasted for 45 minutes.
Then she read a book for 35 minutes.
What time did she finish her swimming lesson and what time did she finish reading
Answers
Answer:
She finished swimming lesson at 2:15 p.m.
and reading book at 2:50 p.m.
Step-by-step explanation:
I hope this helped (:
Lola finished her swimming lesson at 2:15 p.m. and read a book at 2:50 p.m.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
Lola's swimming class began at 1:30 p.m. and lasted 45 minutes.
She then spent 35 minutes reading a book.
To determine the time did she finish her swimming lesson and the time did she finish reading.
swimming end time = began time + class duration
swimming end time = 1:30 p.m. + 45 minutes
swimming end time = 2:15 p.m.
reading end time = began time + reading duration
reading end time = 2:15 p.m. + 35 minutes
reading end time = 2:50 p.m.
Thus, she finished her swimming lesson at 2:15 p.m. and read a book at 2:50 p.m.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
Need help with this, explaining how to do it would be very much appreciated. Thanks :)
Answers
Exactly one solution
Answer:
Solution: There is exactly one solution, the lines intercept at one point, they are not the same line, so they do not have infinite solutions, and if they were to not intercept, they would have no solution.
Step-by-step explanation:
Set the equations equal
-2x-4=3x+3
+4 +4
-2x=3x+7
-3x -3x
-5x=7
/-5
x=-7/5
Plug x back into one of the equations
y=-2(-7/5)-4
y=-6/5
What is the perimeter of a square with a side length of 46 mm?
A. 50 mm B. 100 mm C. 184 mm D. 230 mm
Answers
Answer:
C: 184 mm
Step-by-step explanation:
46*4 = 184
46x4
Given the conversion factor 12 in/ 1 ft, which has the larger volume?
O A. Cube A
O B. Cube B
O C. They are the same size.
Answers
Answer:
A. Cube A
Given:
Cube A volume = 5832 in³
For Cube B dimension in inches:
1.2 feet = 14.4 in1 feet = 12 in1 feet = 12 inSo Volume of Cube B:
L × B × H = 14.4 × 12 × 12 = 2073.6 in³
Cube A has a larger volume that Cube B.