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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 16 (page 651)

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

Short Answer

Expert verified

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

Step by step solution

01

. Given information

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

We have to simplify the given rational expression using factors.

02

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 $\begin{array}{rcl} \frac{x^{3} - 2 x^{2} - 25 x + 50}{x^{2} - 25} & = & \frac{x^{2} (x - 2) - 25 (x - 2)}{(x^{2} - 25)} \\ = & \frac{(x - 2) (x^{2} - 25)}{(x^{2} - 25)} \sin c e (x - 2) i s t h e c o m m o n f a c t o r i n t h e n u m e r a t o r \\ = & (x - 2) \end{array}$

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