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Natural Numbers

Solve a3-275...

Question

Solve
$\frac{a^{3} - 27}{5 a^{2} - 16 a + 3} \div \frac{a^{2} + 3 a + a}{25 a^{2} - 1}$

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Solution

$\frac{a^{3} - 27}{{5 a}^{2} - 16 a + 3} \div \frac{a^{2} + 3 a + 2}{{25 a}^{2} - 1}$
$= \frac{a^{3} - 27}{{5 a}^{2} - 16 a + 3} \times \frac{{25 a}^{2} - 1}{a^{2} + 3 a + 9}$
$= \frac{(a - 3) (a^{2} + 3 a + 9)}{(5 a - 1) (a - 3)} \times \frac{(5 a + 1) (5 a - 1)}{(a^{2} + 3 a + 9)}$
$= (5 a + 1)$

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Similar questions

\frac{a^{3} - 27}{5 a^{2} - 16 a + 3} \div \frac{a^{2} + 3 a + 9}{25 a^{2} - 1}

\frac{a^{3} - 27}{25 a^{2} - 5 a + 1} \div \frac{a^{2} + 3 a + 9}{125 a^{3} + 1}

\frac{a^{3} - 27}{5 a^{2} - 16 a + 3} \div \frac{a^{2} + 3 a + 9}{25 a^{2} - 1}

a^{2} + \frac{1}{a^{2}} - 2 - 3 a + \frac{3}{a}

Q. Solve the following equation,

(a^{2} - 9) x = a^{3} + 27.

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