Question 15

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waecmaths question: 

Simplify $\frac{2{{x}^{2}}-5x-12}{4{{x}^{2}}-9}$

Option A: 

$\frac{x+4}{2x+3}$ 

Option B: 

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

Option C: 

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

Option D: 

$\frac{x-4}{2x-3}$

waecmaths solution: 

$\begin{align}  & \frac{2{{x}^{2}}-5x-12}{4{{x}^{2}}-9}=\frac{2{{x}^{2}}-8x+3x-12}{{{(2x)}^{2}}-{{3}^{2}}}=\frac{2x(x-4)+3(x-4)}{(2x-3)(2x+3)} \\ & \frac{2{{x}^{2}}-5x-12}{4{{x}^{2}}-9}=\frac{(2x+3)(x-4)}{(2x-3)(2x+3)}=\frac{x-4}{2x-3} \\\end{align}$

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