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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q148E. (page 669)

Explain how you find the least common denominator of $x^{2} + 5 x + 4$ and $x^{2} - 16$ .

Short Answer

Expert verified

$(x + 4) (x - 4) (x + 1)$

Step by step solution

01

Step 1. Given information.

The following denominators are given:

$x^{2} + 5 x + 4 x^{2} - 16$

02

Step 2. Finding the least common denominator.

Factor the two denominators:

$x^{2} + 5 x + 4 = (x + 4) (x + 1) x^{2} - 16 = (x + 4) (x - 4)$

Find the LCM of the two denominators:

$(x + 4) (x - 4) (x + 1)$

The least common denominator is equal to the LCM of the two denominators.

So, the least common denominator of the two denominators will be $(x + 4) (x - 4) (x + 1)$

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Most popular questions from this chapter

In the following exercises, perform the indicated operations

$\frac{5 q}{p^{2} q - p^{2}} + \frac{4 q}{q^{2} - 1}$

Solve the equation $c = \frac{2}{a} + \frac{b}{5}$ for the variable $a$ .

In the following exercise, perform the indicated operation:

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For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} 梅 \frac{5 m^{2} + 10 m}{2 m - 10}$

Solve each rational function inequality and write the solution in interval notation. Given the function $R (x) = \frac{(x + 1)}{(x - 4)},$ find the values of x that make the function less than or equal to 0.

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