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Question
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
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Solution
It is known that,
a2 − b2 = (a + b) (a − b)
\[\ \frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
\[ = \frac{4 x^2 - 8x - 3x + 6}{\left(4x \right)^2 - \left(3 \right)^2}\]
\[ = \frac{4x\left(x - 2 \right) - 3\left(x - 2 \right)}{\left(4x + 3 \right)\left(4x - 3 \right)}\]
\[ = \frac{\left(4x - 3 \right)\left(x - 2 \right)}{\left(4x + 3 \right)\left( 4x - 3 \right)}\]
\[ = \frac{x - 2}{4x + 3}\]
RELATED QUESTIONS
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Factorise:
y3 − 27
Factorise:
27m3 − 216n3
Factorise:
343a3 − 512b3
Simplify:
(a + b)3 − a3 − b3
Simplify:
(3xy − 2ab)3 − (3xy + 2ab)3
Factorise: x3 - 8y3
Factorise: 54p3 - 250q3.
Factorise the following:
27x3 – 8y3
