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प्रश्न
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
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उत्तर
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ \frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
\[ = \frac{x^2 - 8x + 3x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x \right)^2 - \left( 8 \right)^2}{\left( x - 8 \right)^2}\]
\[ = \frac{x\left( x - 8 \right) + 3\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}\]
\[ = \frac{\left( x + 3 \right)\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}\]
= 1
संबंधित प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
27m3 − 216n3
Simplify:
(a + b)3 − a3 − b3
Simplify:
(3xy − 2ab)3 − (3xy + 2ab)3
Factorise: x3 - 8y3
Factorise: 54p3 - 250q3.
Simplify: (2x + 3y)3 - (2x - 3y)3
Factorise the following:
27x3 – 8y3
