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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q7.52TI. (page 1069)

Simplify the complex rational expression by writing it as division:
$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$

Short Answer

Expert verified

$\frac{a b}{b - a}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$

02

Step 2. Simplification of the complex rational expression.

Find the common denominators for the numerator and the denominator:

$\frac{\frac{1 . b}{a . b} + \frac{1 . a}{b . a}}{\frac{1 . b^{2}}{a^{2} . b^{2}} - \frac{1 . a^{2}}{b^{2} . a^{2}}}$

Simplify the numerator and the denominator:

$\frac{\frac{b}{a b} + \frac{a}{a b}}{\frac{b^{2}}{a^{2} b^{2}} - \frac{a^{2}}{a^{2} b^{2}}} \frac{\frac{b + a}{a b}}{\frac{b^{2} - a^{2}}{a^{2} b^{2}}}$

Rewrite as a division problem:

$\frac{b + a}{a b} 梅 \frac{b^{2} - a^{2}}{a^{2} b^{2}}$

Rewrite as the product of the first and the reciprocal of the second:

$\frac{b + a}{a b} . \frac{a^{2} b^{2}}{b^{2} - a^{2}}$

Factorise the terms (where possible), cancel the common factors from the numerator and the denominator and simplify:

localid="1662391087352" $\frac{b + a}{a b} . \frac{a b . a b}{(b + a) (b - a)} \frac{a b}{b - a}$

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Most popular questions from this chapter

Simplify each expression:

$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$

Divide: $\frac{2 + 4 i}{5 i}$

In the following exercises, factor completely using the difference of squares pattern, if possible.

$a^{2} + 6 a + 9 - 9 b^{2}$

In the following exercises, convert each number to decimal form.

(a) $- 8.3 脳 10^{2}$ (b) $3.8 脳 10^{- 2}$

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