Question

Find $\frac{x}{y}$
$\frac{1}{x+2y}-\frac{2}{x-2y}=\frac{15}{7}$

Answer 1

$\frac{1}{x+2y}-\frac{2}{x-2y}=\frac{15}{7}$

$\Rightarrow \frac{x-2y-2x-4y}{x^2-4y^2}=\frac{15}{7}$

$\Rightarrow \frac{-x-6y}{x^2-4y^2}=\frac{15}{7}$

$\Rightarrow -7x-42y=15x^2-60y^2$

$\Rightarrow 15x^2-7x=-60y^2+42y$

$\Rightarrow x(15x-7)=y(42-60y)$

$\therefore \frac{x}{y}=\frac{42-60y}{15x-7}$