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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 271 (page 966)

Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify.
$\frac{\frac{1}{3} + \frac{1}{8}}{\frac{1}{4} + \frac{1}{12}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{11}{8}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{3} + \frac{1}{8}}{\frac{1}{4} + \frac{1}{12}}$

02

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is 24. Clear the fractions by multiplying the numerator and denominator by that LCD.
$= \frac{24 路 (\frac{1}{3} + \frac{1}{8})}{24 路 (\frac{1}{4} + \frac{1}{12})} = \frac{24 路 \frac{1}{3} + 24 路 \frac{1}{8}}{24 路 \frac{1}{4} + 24 路 \frac{1}{12}} = \frac{8 + 3}{6 + 2} = \frac{11}{8}$

03

Step 3. Conclusion.

The simplified form of the given expression is $\frac{11}{8}$ .

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Most popular questions from this chapter

Simplify

In the following exercises, use either method.

$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

. 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.

$\frac{3}{7} + \frac{2}{3} = \frac{1}{w}$

In the following exercises, solve.

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

In the following exercises, solve.

$\frac{3}{r + 10} - \frac{4}{r - 4} = 1$

See all solutions

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