Solve 2(1/x-y)(1/x+y)

$$2( \frac{ 1 }{ x-y } )( \frac{ 1 }{ x+y } )$$

Evaluate

$$\frac{2}{x^{2}-y^{2}}$$

Solution Steps

Express 2\times \frac{1}{x-y} as a single fraction.

$$\frac{2}{x-y}\times \frac{1}{x+y}$$

Multiply \frac{2}{x-y} times \frac{1}{x+y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{\left(x-y\right)\left(x+y\right)}$$

Consider \left(x-y\right)\left(x+y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2}{x^{2}-y^{2}}$$

Differentiate w.r.t. x

$$-\frac{4x}{\left(x^{2}-y^{2}\right)^{2}}$$