Q40. - Algebra 2

Question

Simplify each expression.

 

$-\frac{x^2-y^2}{x+y}·\frac{1}{x-y}$

Step-by-Step Solution

Answer

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

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:

 

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

Step 3. Conclusion .

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