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Addition of Rational Expressions

Evaluate: x+...

Question

Evaluate:

$\frac{x + 2}{(x + 1) (2 x + 3)} - \frac{2 x + 3}{(x + 1) (x + 2)} + \frac{3 x + 5}{(2 x + 3) (x + 2)}$

A

2x

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B

-1

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C

0

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D

x

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Solution

The correct option is A 0
Given, $\frac{x + 2}{(x + 1) (2 x + 3)} - \frac{2 x + 3}{(x + 1) (x + 2)} + \frac{3 x + 5}{(2 x + 3) (x + 2)}$
$\Rightarrow \frac{{(x + 2)}^{2} - {(2 x + 3)}^{2} + (3 x + 5) (x + 1)}{(x + 1) (x + 2) (2 x + 3)}$
$\Rightarrow \frac{(x^{2} + 4 x + 4) - (4 x^{2} + 12 x + 9) + (3 x^{2} + 8 x + 5)}{(x + 1) (x + 2) (2 x + 3)}$
$\Rightarrow \frac{x^{2} + 4 x + 4 - 4 x^{2} - 12 x - 9 + 3 x^{2} + 8 x + 5}{(x + 1) (x + 2) (2 x + 3)}$
$\Rightarrow \frac{0}{(x + 1) (x + 2) (2 x + 3)} = 0$

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