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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. 39 (page 1069)

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

Short Answer

Expert verified

The simplified expression is $\frac{(5 c^{2} + 9 c + 2) (c + 5)}{(3 c + 1) {(c - 5)}^{2}} .$

Step by step solution

01

Step 1. Given Information.

$\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

02

Step 2. Factor each numerator and denominator completely

$c^{2} + 10 c + 25 = (c + 5) (c + 5) c^{2} - 25 = (c - 5) (c + 5) 3 c^{2} - 14 c - 5 = (3 c + 1) (c - 5)$

Then, multiply the numerators and denominators.

$\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5} = \frac{5 c^{2} + 9 c + 2}{(c - 5) (c + 5)} . \frac{(c + 5) (c + 5)}{(3 c + 1) (c - 5)}$

03

Step 3. Simplify by dividing out common factors

$\frac{(5 c^{2} + 9 c + 2) (c + 5)}{(3 c + 1) {(c - 5)}^{2}} .$

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Most popular questions from this chapter

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

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

Simplify::
(a) $36^{\frac{1}{2}}$

(b) $8^{\frac{1}{3}}$

(c) $16^{\frac{1}{4}}$

Simplify:

$(6 - 3 \sqrt{7}) (3 + 4 \sqrt{7})$
$(\sqrt[3]{x} - 2) (\sqrt[3]{x} - 3)$

Simplify-

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

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

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

Factor Trinomials of the Form $a x^{2} + b x + c$ using the 鈥榓c鈥� Method.

$5 s^{2} 鈭� 9 s + 4$

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