Question

solve the equation x+1/x-1 + x-2/x+2=3 for x
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Answer 1

Step-by-step explanation:

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

x² + 2x + x + 2 + x² - 2x - x + 2 / x² + 2x - x - 2 = 3

2x² + 4 / x² - x - 2 = 3

2x² + 4 = 3 (x² - x - 2)

2x² + 4 = 3x² - 3x - 6

- x² = - 3x - 10

- x² + 3x + 10 = 0

- x² + 5x - 2x + 10 = 0

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

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

x = -2 or 5