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Question
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
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:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Simplify:
\[\frac{1 - 2x + x^2}{1 - x^3} \times \frac{1 + x + x^2}{1 + x}\]
Factorise:
343a3 − 512b3
Simplify:
(x + y)3 − (x − y)3
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify:
(a + b)3 − a3 − b3
Factorise: x3 - 8y3
Factorise: `a^3 - 1/(a^3)`
Simplify: (a - b)3 - (a3 - b3)
Factorise the following:
27x3 – 8y3
