Question

Combine the following fractions by addition or subtraction as directed.

Answer 1

Answer:$\frac{6}{y^2-xy}-\frac{6}{x^2-xy}=\frac{6(x+y)}{xy(y-x)}$

Explanation:

Combining the fractions, we have:

$\begin{gathered} \frac{6(x^2-xy)-6(y^2-xy)}{(x^2-xy)(y^2-xy)} \\ \\ =\frac{6x^2-6xy-6y^2+6xy}{(x^2-xy)(y^2-xy)} \\ \\ =\frac{6x^2-6y^2}{x(x-y).y(y-x)} \\ \\ =\frac{6(x-y)(x+y)}{-xy(x-y)^2} \\ \\ =\frac{-6(x+y)}{xy(x-y)} \\ \\ =\frac{6(x+y)}{xy(y-x)} \end{gathered}$