Question

Solve the following pairs of equation by reducing them to a pair of linear equation
$\frac{10}{x+y}+\frac{2}{x-y}=4$

Answer 1

$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\Rightarrow \frac{10(x-y)+2(x+y)}{(x+y)(x-y)}=4$
$\Rightarrow 10x-10y+2x+2y=4(x^2-y^2)$
$\Rightarrow 12x-8y=4(x^2-y^2)$
$\Rightarrow 12x-8y=4x^2-4y^2$
$\Rightarrow 4y^2-4x^2+12x-8y=0$
$\Rightarrow y^2-x^2+3x-2y=0$.