Divide $4 (2 x^{2} + 5 x + 3)$ by $2 (2 x + 3)$

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Solution

$\frac{4 (2 x^{2} + 5 x + 3)}{2 (2 x + 3)} = \frac{2 (2 x^{2} + 5 x + 3)}{2 x + 3}$
$\frac{2 (2 x^{2} + 3 x + 2 x + 3)}{(2 x + 3)} = \frac{2 [x (2 x + 3) + 1 (2 x + 3)]}{2 x + 3}$
$\frac{2 (2 x + 3) [(x + 1)]}{(2 x + 3)} = 2 (x + 1)$
$\Rightarrow 2 (x + 1)$

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