Question

Simplify each expression.

$-\frac{x^2-y^2}{x+y}·\frac{1}{x-y}$

Short answer

The simplified value of expression is $-\frac{x^2-y^2}{x+y}·\frac{1}{x-y}=-1$.

Step-by-step solution

Step 1. Given Information.

The given expression to simplify is $-\frac{x^2-y^2}{x+y}·\frac{1}{x-y}$.

Step 2. Calculation.

Simplifying the expression:

$\begin{array}{l}-\frac{x^2-y^2}{x+y}\cdot \frac{1}{x-y}=-\frac{x^2-y^2}{\left(x+y\right)\left(x-y\right)}\\ -\frac{x^2-y^2}{x+y}\cdot \frac{1}{x-y}=-\frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}\left(\text{Factoringthenumerator}\right)\\ -\frac{x^2-y^2}{x+y}\cdot \frac{1}{x-y}=-1\end{array}$

Step 3. Conclusion.

The simplified value of expression is $-\frac{x^2-y^2}{x+y}\cdot \frac{1}{x-y}=-1$.