Solve 8x^2y^2/x^2-y^2div2xy/{x^2-{y}^2}

$$\frac{ 8 { x }^{ 2 } { y }^{ 2 } }{ { x }^{ 2 } - { y }^{ 2 } } \div \frac{ 2xy }{ { x }^{ 2 } - { y }^{ 2 } }$$

Evaluate

$$4xy$$

Solution Steps

Divide \frac{8x^{2}y^{2}}{x^{2}-y^{2}} by \frac{2xy}{x^{2}-y^{2}} by multiplying \frac{8x^{2}y^{2}}{x^{2}-y^{2}} by the reciprocal of \frac{2xy}{x^{2}-y^{2}}.

$$\frac{8x^{2}y^{2}\left(x^{2}-y^{2}\right)}{\left(x^{2}-y^{2}\right)\times 2xy}$$

Cancel out 2xy\left(x^{2}-y^{2}\right) in both numerator and denominator.

$$4xy$$

Differentiate w.r.t. x

$$4y$$