solve for x

Question

x/x-2 + x-1/x+1 = -1

Answer 1

x = -2 or x = 4

Answer 2

make step by step

Answer 3

Sure! Let's solve for x step by step.

Given equation:
x/(x-2) + (x-1)/(x+1) = -1

Step 1: Find a common denominator for the fractions on the left side. The common denominator is (x-2)(x+1):
x(x+1)/[(x-2)(x+1)] + (x-1)(x-2)/[(x-2)(x+1)] = -1

Step 2: Combine the fractions by adding them:
[x(x+1) + (x-1)(x-2)] / [(x-2)(x+1)] = -1

Step 3: Simplify the numerator:
[x^2 + x + x^2 - 3x + 2] / [(x-2)(x+1)] = -1
[(2x^2 - 2x + 2)] / [(x-2)(x+1)] = -1

Step 4: Multiply both sides by the denominator:
2x^2 - 2x + 2 = - (x^2 - x - 2)

Step 5: Expand and simplify both sides:
2x^2 - 2x + 2 = -x^2 + x + 2
2x^2 - 2x + 2 = -x^2 + x + 2
3x^2 - 3x = 0

Step 6: Factor out x:
3x(x - 1) = 0

Step 7: Set each factor to zero and solve for x:
3x = 0 -> x = 0
x - 1 = 0 -> x = 1

Therefore, the solutions to the equation x/(x-2) + (x-1)/(x+1) = -1 are x = 0 and x = 1.