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प्रश्न
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
उत्तर
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ \frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
\[= \frac{a^2 + 7a + 3a + 21}{a^2 + 7a - a - 7} \times \frac{\left(a + 1 \right)\left(a - 1 \right)}{\left(a + 3 \right)}\]
\[= \frac{a\left(a + 7 \right) + 3\left(a + 7 \right)}{a \left(a + 7 \right) - 1\left(a + 7 \right)} \times \frac{\left(a + 1 \right)\left(a - 1 \right)}{\left(a + 3 \right)}\]
\[ = \frac{\left(a + 7 \right)\left(a + 3 \right)}{\left(a - 1 \right)\left(a + 7 \right)} \times \frac{\left(a + 1 \right)\left(a - 1 \right)}{\left(a + 3 \right)}\]
= (a + 1)
संबंधित प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
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:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Factorise:
x3 − 64y3
Factorise:
27m3 − 216n3
Factorise:
`16a^3 - 128/b^3`
Simplify:
p3 − (p + 1)3
Factorise: x3 - 8y3
Factorise: 54p3 - 250q3.
Simplify: (a - b)3 - (a3 - b3)
