Simplify $\dfrac{9x^2 - 4}{12x^2 - x - 6}$ . Answer ...

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Worked solution

1. Factorise the numerator using difference of two squares.

$9x^2-4=(3x)^2-2^2=(3x-2)(3x+2)$

2. Factorise the quadratic denominator.

$12x^2-x-6=(3x-2)(4x+3)$

since $3x\cdot4x=12x^2$ and $9x-8x=x$ .

3. Cancel the common factor and write the simplified algebraic fraction.

$\frac{9x^2-4}{12x^2-x-6}=\frac{(3x-2)(3x+2)}{(3x-2)(4x+3)}=\frac{3x+2}{4x+3}$

Answer

$\dfrac{3x+2}{4x+3}$

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