Question

The simplified form of $(\frac{x(x-5y)}{x^2-6xy+5y^2}\times \frac{(x+y)(x-y)}{x^2+xy})$ is

Answer 1

$\frac{x(x-5y)}{x^2-6xy+5y^2}\times \frac{(x+y)(x-y)}{x^2+xy}$

$\Rightarrow \frac{x(x-5y)}{x^2-xy-5xy+5y^2}\times \frac{(x+y)(x-y)}{x(x+y)}$

$\Rightarrow \frac{x(x-5y)}{x(x-y)-5y(x-y)}\times \frac{(x+y)(x-y)}{x(x+y)}$

$\Rightarrow \frac{x(x-5y)}{(x-5y)(x-y)}\times \frac{(x+y)(x-y)}{x(x+y)}$

$=1$.