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Question
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Solution
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)
RELATED QUESTIONS
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\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
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\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
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\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
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\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
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\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
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343a3 − 512b3
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(3a + 5b)3 − (3a − 5b)3
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