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Solving Equations with Variable on Both Sides

Solve 2+ 2x...

Question

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

A

\frac{2}{3}

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B

\frac{- 2}{3}

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C

\frac{3}{3}

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D

- 3

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Solution

The correct option is D $- 3$
$2 + \frac{2 x - 3}{2 x + 3} = \frac{3 x + 4}{x + 2}$
multiply above equation by $(2 x + 3) (x + 2)$
$\Rightarrow 2 (2 x + 3) (x + 2) + (2 x - 3) (x + 2) = (3 x + 4) (2 x + 3)$
$\Rightarrow (4 x^{2} + 14 x + 12) + (2 x^{2} + x - 6) = (6 x^{2} + 17 x + 12)$
$\Rightarrow 15 x - 17 x 12 - 6$
$\Rightarrow - 2 x = 6$
$\Rightarrow x = - \frac{6}{2}$
$∴ x = - 3$

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