2+(4/x-1)=4/(x^2-x)
Please help solve for x, I was stuck at this problem
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
[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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