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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 15 (page 1069)

Simplify the rational expression $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} .$

Short Answer

Expert verified

Simplified form of the given rational expression $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} i s \frac{p^{2} + 4}{p - 2}; p 鈮� 2$ $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} i s \frac{(p^{2} + 4)}{(p - 2)} .$

Step by step solution

01

Step 1. Given information

Given rational expression is $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} .$

We have to simplify the the given expression.

02

Step 2. Simplification of the rational expression

For simplification factor, the numerator and denominator separately, find the common factor and then simplify.

Hence simplified form is $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} = \frac{p^{2} (p + 3) + 4 (p + 3)}{(p + 3) (p - 2)} = \frac{(p + 3) (p^{2} + 4)}{(p + 3) (p - 2)} = \frac{p^{2} + 4}{P - 2}; p 鈮� 2$

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Most popular questions from this chapter

Simplify

(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Factor by Grouping
In the following exercises, factor by grouping.

$r^{2} 鈭� 3 r 鈭� r + 3$ .

Simplify-

(a) $\sqrt{75 a^{9}}$

(b) $\sqrt[3]{128 m^{11}}$

(c) $\sqrt[4]{62 n^{7}}$

In the following exercises, simplify each expression using the properties for exponents.

$鈸� q^{27} 路 q^{15} 鈸� 5^{x} 路 5^{4 x} 鈸� 9 u^{41} 路 7 u^{53} 鈸� c^{5} 路 c^{11} 路 c^{2}$

Use the Zero Product Property in the following exercises to solve.

$(a - 3) (a + 7) = 0$

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