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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 430 (page 737)

In the following exercise, Simplify.
$\frac{\frac{2}{m} + \frac{m}{n}}{\frac{n}{m} - \frac{1}{n}}$

Short Answer

Expert verified

The solution is $\frac{2 n + m^{2}}{n^{2} - m}$

Step by step solution

01

Step 1. Given information

$\frac{\frac{2}{m} + \frac{m}{n}}{\frac{n}{m} - \frac{1}{n}}$

02

Step 2. Simplify

The LCD of all the fractions is $n m$

Multiply both the numerator and denominator by $n m$

role="math" localid="1646724306783" $= \frac{n m (\frac{2}{m} + \frac{m}{n})}{n m (\frac{n}{m} - \frac{1}{n})} = \frac{\frac{2 n + m^{2}}{m n}}{\frac{n^{2} - m}{m n}}$

Rewrite as fraction division.

role="math" localid="1646724387368" $= \frac{2 n + m^{2}}{m n} 梅 \frac{n^{2} - m}{m n}$

Multiply the first the reciprocal of second

$= \frac{2 n + m^{2}}{m n} 脳 \frac{m n}{n^{2} - m} = \frac{2 n + m^{2}}{n^{2} - m}$

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}$

Determine the values for which the rational expression is undefined.

$\frac{b - 7}{b^{2} - 25} .$

In the following expression, perform the indicated operation:

$\frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a^{2} - 2 a}$

Simplify the rational expression $\frac{12 p - 240}{5 p - 100} .$

In the following exercises, divide the rational expressions.

$\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

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