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Question

2/(x^2-X)=1/X+4/(x^2-1)

Answer 1

1/x + 4/(x² - 1) = 2/(x² - x)

 

(x² - 1)/[x(x² - 1)] + 4x/[x(x² - 1)] = 2/(x² - x)

 

(x² + 4x - 1)/[x(x² - 1)] = 2/(x² - x)

 

(x² + 4x - 1)(x² - x) = 2x(x² - 1)

 

x⁴ + 3x³ - 5x² + x = 2x³ - 2x

 

x⁴ + x³ - 5x² + 3x = 0

 

x(x - 1)²(x + 3) = 0

 

However, from the original equation, we see that x ≠ 0 and x ≠ 1.

 

So the only solution is x = -3.