Answer:
x = 0 or x = 1
Explanation:
(x)/(x - 2) + (x - 1)/(x + 1) = -1
The LCD is (x - 2)(x + 1).
Multiply both sides of the equation by the LCD.
(x - 2)(x + 1) × (x)/(x - 2) + (x - 2)(x + 1) × (x - 1)/(x + 1) = (x - 2)(x + 1) × (-1)
The factors in bold cancel out of each product.
x(x + 1) + (x - 2)(x - 1) = -(x - 2)(x + 1)
x² + x + x² - x - 2x + 2 = -(x² + x - 2x - 2)
2x² - 2x + 2 = -x² + x + 2
3x² - 3x = 0
3x(x - 1) = 0
x = 0 or x = 1
The restrictions on the domain are:
x - 2 = 0
x = 2
x + 1 = 0
x = -1
Since our solutions do not include the excluded values, x = 2 and x = -1, both solutions x = 0 and x = 1 are valid.
Answer: x = 0 or x = 1