Q41. - Algebra 2

Question

Simplify each expression.

 

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

Step-by-Step Solution

Answer

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

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:

 

 $\begin{array}{l}\frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x^2}{x^2-25y^2}\cdot \frac{5y-x}{x}\left(\text{Writing the denominator as a product of reciprocal}\right)\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x^2\left(5y-x\right)}{\left(x^2-25y^2\right)x}\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=\frac{x\cdot x\cdot -\left(x-5y\right)}{\left(x-5y\right)\left(x+5y\right)x}\left(\text{Factoring the numerator and denominator}\right)\\ \frac{\frac{x^2}{x^2-25y^2}}{\frac{x}{5y-x}}=-\frac{x}{x+5y}\left(\text{Cancelling out the common terms from numerator and denominator}\right)\end{array}$

Step 3. Conclusion .

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