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Method of Intervals

Solve for x :...

Question

Solve for x : $2 + \frac{2 x - 3}{2 x + 3} = \frac{3 x + 4}{x + 2}$

A

7

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B

13

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C

- 12

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D

- 3

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Solution

The correct option is C $- 3$
$2 + \frac{2 x - 3}{2 x + 3} = \frac{3 x + 4}{x + 2}$

$\Rightarrow \frac{2 (2 x + 3) + (2 x - 3)}{2 x + 3} = \frac{3 x + 4}{x + 2}$

$\Rightarrow \frac{6 x + 3}{2 x + 3} = \frac{3 x + 4}{x + 2}$

$\Rightarrow (6 x + 3) (x + 2) = (3 x + 4) (2 x + 3) \Rightarrow 6 x^{2} + 15 x + 6 = 6 x^{2} + 17 x + 12$

$\Rightarrow - 2 x = 6 \Rightarrow x = - 3$

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