Question

Factorise
$\frac{a^3}{b^3}+\frac{b^3}{c^3}+\frac{c^3}{a^3}-3$

Answer 1

$\frac{a^3}{b^3}+\frac{b^3}{c^3}+\frac{c^3}{a^3}-3$
$={\left(\frac{a}{b}\right)}^3+{\left(\frac{b}{c}\right)}^3+{\left(\frac{c}{a}\right)}^3-3\left(\frac{a}{b}\right)\left(\frac{b}{c}\right)\left(\frac{c}{a}\right)$
$=(\frac{a}{b}+\frac{b}{c}+\frac{c}{a})(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2})$