Question

Simplify:

\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]

Answer 1

It is known that,

a² − b² = (a + b) (a − b)

\[\ \frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]

\[ = \frac{4 x^2 - 8x - 3x + 6}{\left(4x \right)^2 - \left(3 \right)^2}\]

\[ = \frac{4x\left(x - 2 \right) - 3\left(x - 2 \right)}{\left(4x + 3 \right)\left(4x - 3 \right)}\]

\[ = \frac{\left(4x - 3 \right)\left(x - 2 \right)}{\left(4x + 3 \right)\left( 4x - 3 \right)}\]

\[ = \frac{x - 2}{4x + 3}\]