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Linear Equation

Solve for x:3...

Question

Solve for $x$ :
$\frac{3}{x + 1} - \frac{2}{x - 1} = \frac{5}{x^{2} - 1}$

A

9

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B

10

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C

12

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D

8

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Solution

The correct option is B 10
$\frac{3}{x + 1} - \frac{2}{x - 1} = \frac{5}{x^{2} - 1}$
$\Rightarrow \frac{3 (x - 1) - 2 (x + 1)}{(x + 1) (x - 1)} = \frac{5}{x^{2} - 1}$
$\Rightarrow \frac{3 x - 3 - 2 x - 2}{x^{2} - 1} = \frac{5}{x^{2} - 1}$
As $x \neq \pm 1$
$\Rightarrow x - 5 = 5$
$\Rightarrow x = 10$

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