Please help solve 2+(4/x-1)=4/(x^2-x)
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Please help solve 2+(4/x-1)=4/(x^2-x)

[From: ] [author: ] [Date: 11-12-10] [Hit: ]
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2+(4/x-1)=4/(x^2-x)
Please help solve for x, I was stuck at this problem

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Add the left side first. Multiply the 2 by (x - 1)/(x - 1) to get a common denominator:

[2(x - 1) / (x - 1)] + [4 / (x - 1)] =

(2x - 2 + 4) / (x - 1)

Simplify the numerator:

(2x + 2) / (x - 1)


Next, factor the denominator on the right:

4 / x(x - 1)

Rewrite the equation:

(2x + 2) / (x - 1) = 4 / x(x - 1)

Multiply both sides by (x - 1):

2x + 2 = 4/x

Multiply both sides by x:

2x^2 + 2x = 4

Divide through by 2:

x^2 + x = 2

Subtract 2 from both sides:

x^2 + x - 2 = 0

Factor to:

(x + 2)(x - 1) = 0

x = -2 and x = 1

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