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प्रश्न
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
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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:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
y3 − 27
Factorise:
125y3 − 1
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
`16a^3 - 128/b^3`
Factorise: x3 - 8y3
Factorise: 27p3 - 125q3.
Factorise: 54p3 - 250q3.
