Question

Simplify the rational expression $\frac{x^3-2x^2-25x+50}{x^2-25}$

Short answer

Simplified form of rational expression$\frac{x^3-2x^2-25x+50}{x^2-25}is(x-2)$

Step-by-step solution

.  Given information 

Given rational expression is $\frac{x^3-2x^2-25x+50}{x^2-25}$.

We have to simplify the given rational expression using factors.

Step 2.  Simplification of  the rational expression

To simply first we have to factor the numerator by grouping factor and then simplify.

Thus the simplified form is$\begin{array}{rcl}\frac{x^3-2x^2-25x+50}{x^2-25}& =& \frac{x^2(x-2)-25(x-2)}{(x^2-25)}\\ & =& \frac{(x-2)(x^2-25)}{(x^2-25)}\sin ce(x-2)isthecommonfactorinthenumerator\\ & =& (x-2)\end{array}$