Question

Simplify each expression.

$\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}$

Short answer

The simplified value of expression is$\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=-\frac{x}{x+5y}$.

Step-by-step solution

Step 1. Given Information.

The given expression to simplify is $\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}$.

Step 2. Calculation.

Simplifying the expression:

$\begin{array}{l}\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x^2}{x^2-25y^2}\cdot \frac{5y-x}{x}\left(\text{Writingthedenominatorasaproductofreciprocal}\right)\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x^2\left(5y-x\right)}{\left(x^2-25y^2\right)x}\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x\cdot x\cdot -\left(x-5y\right)}{\left(x-5y\right)\left(x+5y\right)x}\left(\text{Factoringthenumeratoranddenominator}\right)\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=-\frac{x}{x+5y}\left(\text{Cancellingoutthecommontermsfromnumeratoranddenominator}\right)\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=-\frac{x}{x+5y}$.