Q11. - Algebra 1

Question

Simplify each expression.

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

Step-by-Step Solution

Answer

$\mathit{x}\mathbf{+}\mathbf{5}$

Step 1. Division expression.

Write as a division expression.

$\frac{x^2-25}{x-2}÷\frac{x-5}{x-2}$

Step 2. Divide.

To divide, multiply by the reciprocal.

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

Step 3. Factor.

Factor the given expression and simplify.

$\frac{\left(x+5\right)\left(x-5\right)}{\left(x-2\right)}\cdot \frac{\left(x-2\right)}{\left(x-5\right)}=x+5$

Therefore, $\frac{\frac{x^2-25}{x-2}}{\frac{x-5}{x-2}}$ can be simplified as $x+5$.