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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.64 (page 935)

Add: $\frac{x^{2} + 8 x}{x + 5} + \frac{15}{x + 5}$

Short Answer

Expert verified

The required expression is $x + 3$ .

Step by step solution

01

Given Information

The given expression is,

$\frac{x^{2} + 8 x}{x + 5} + \frac{15}{x + 5}$

02

Simplifying the expression

Make common denominator:

\frac{x^{2} + 8 x + 15}{x + 5}

Factor the numerator:

$\frac{(x + 5) (x + 3)}{x + 5}$

Cancel the like factor from the numerator and denominator:

$x + 3$

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Most popular questions from this chapter

In the following exercises, simplify.

$\frac{a^{2} - a - 12}{a^{2} - 8 a + 16}$

. In this section, you learned to simplify the complex fraction $\frac{\frac{3}{x + 2}}{\frac{x}{x^{2} - 4}}$

two ways: rewriting it as a division problem multiplying the numerator and denominator by the LCD Which method do you prefer? Why?

In the following exercises, solve.

$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$

In the following exercises, solve.

$\frac{4}{5} + \frac{1}{4} = \frac{2}{v}$

Ironing Lenore can do the ironing for her family’s business in h hours. Her daughter would take h + 2 hours to get the ironing done. If Lenore and her daughter work together, using 2 irons, the number of hours it would take them to do all the ironing is $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .

Simplify the complex fraction $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .
Find the number of hours it would take Lenore and her daughter, working together, to get the ironing done if $h = 4$ .

See all solutions

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