Solve the following equation. Show all your work.
(x)/(x-2)+(x-1)/(x+1)=-1
(x)/(x-2)+(x-1)/(x+1)=-1
clear the fractions by multiplying by the common denominator of (x-2)(x+1) and you have
(x)(x+1) + (x-1)(x-2) = -(x-2)(x+1)
x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2
3x^2 - 3x = 0
x(x-1) = 0
x = 0,1
This one is ok, but you should always check for extraneous roots. In this case that would be x = -1,2 since the original equation would be undefined for those values.
please help me
Thank you so much!
x=0, or x=1
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Type in "x/x-2+(x-1)/x+1=-1" and click on step by step and just use that as your answer.
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Solve the following equation. Show all your work.
(x)/(x-2)+(x-1)/(x+1)=-1
(x)/(x-2)+(x-1)/(x+1)=-1
To solve this, we first need to find a common denominator for the two fractions on the left side of the equation. Since the denominators are (x-2) and (x+1), the common denominator is (x-2)(x+1).
Multiplying both sides of the equation by the common denominator, we get:
(x)(x+1) + (x-1)(x-2) = -1(x-2)(x+1)
Simplifying the left side:
x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2
Combining like terms:
3x^2 - 3x = 0
Factoring out 3x:
3x(x-1) = 0
Now we have two solutions: x=0 and x=1.
However, we need to check whether either of these solutions would result in a denominator of 0, which would make the left side of the equation undefined.
Checking for x=0:
(x)/(x-2)+(x-1)/(x+1)=-1
(0)/(0-2)+(0-1)/(0+1)=-1
-1 = -1
So x=0 is a valid solution.
Checking for x=1:
(x)/(x-2)+(x-1)/(x+1)=-1
(1)/(1-2)+(1-1)/(1+1)=-1
-1/2 = -1
So x=1 is not a valid solution.
Therefore, the only solution to the equation is x=0.
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Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao working together to clean a typical pool? Show all your work. Leave your final answer as an integer or reduced fraction.
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Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao working together to clean a typical pool? Show all your work. Leave your final answer as an integer or reduced fraction.
Sure! Let x be the amount of time it takes for Anita and Chao to clean a typical pool working together.
Anita can clean a pool in 8 hours, so in one hour she can clean 1/8 of a pool. Similarly, Chao can clean 1/6 of a pool in one hour. Together, they can clean:
1/8 + 1/6 = 7/24
of the pool in one hour. Therefore:
7/24 x = 1
Multiplying both sides by the reciprocal of 7/24:
x = 24/7 hours, or approximately 3.43 hours.
Therefore, it would take Anita and Chao approximately 3.43 hours, or 3 hours and 26 minutes, to clean a typical pool working together.
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Simplify 4√6/√30 by rationalizing the denominator. Show your work.