Question

1 question 60 points need help now
Solve the equation and show all your work
$\frac{x}{x-2} + \frac{x-1}{x+1} =-1$

Answer 1

Answer:

The answer to your question is  x = 0 and x = 1

Step-by-step explanation:

Equation

                       $\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1$

1)

                      $\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1$

Expand

2)                  x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)

Simplify

3)                  2x² -2x + 2 = -1(x² + x - 2x - 2)

4)                  2x² - 2x + 2 = -x² + x + 2

Equal to zero

5)                  2x² - 2x + 2 + x² - x - 2 = 0

6)                  3x² - 3x = 0

Factor

7)                  3x(x - 1) = 0

8)                  3x₁ = 0                   x₂ - 1 = 0

9)                    x₁ = 0/3                x₂ = 1

10)                  x₁ = 0                    x₂ = 1