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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.55TI. (page 675)

Simplify the complex rational expression by LCD:
$\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

Short Answer

Expert verified

$\frac{7}{3}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

02

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions in the whole expression is 10.

Clear the fraction by multiplying the numerator and the denominator by the LCD i.e., 10:

$\frac{10 . (\frac{1}{2} + \frac{1}{5})}{10 . (\frac{1}{10} + \frac{1}{5})}$

Distribute:

$\frac{10 . \frac{1}{2} + 10 . \frac{1}{5}}{10 . \frac{1}{10} + 10 . \frac{1}{5}}$

Simplify:

role="math" localid="1644719678072" $\frac{5 + 2}{1 + 2} \frac{7}{3}$

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Most popular questions from this chapter

Solve the proportion $\frac{x}{56} = \frac{7}{8}$ .

In the following exercises, multiply the rational expressions.

$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2} + \frac{12}{x^{2}} > \frac{5}{x}$

In the following exercise, perform the indicated operation:

$\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$

Simplify the complex rational expression by using the LCD:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{a}{b} + \frac{b}{a}}$

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