Question

If $\frac{2}{x+2y}+\frac{1}{x-2y}=\frac{-5}{7}$ then prove that $\frac{x}{y}=\frac{2(10y-7)}{(5x-21)}$

Answer 1

$\frac{2}{x+2y}+\frac{1}{x-2y}=\frac{-5}{7}$

$\Rightarrow \frac{2x-4y+x+2y}{x^2-4y^2}=\frac{-5}{7}$

$\Rightarrow \frac{3x-2y}{x^2-4y^2}=\frac{-5}{7}$

$\Rightarrow 21x-14y=5x^2-20y^2$

$\Rightarrow 5x^2-21x=20y^2-14y$

$\Rightarrow x(5x-21)=2y(10y-7)$

$\therefore \frac{x}{y}=\frac{2(10y-7)}{(5x-21)}$