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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. 8.139 (page 981)

Solve: $\frac{1}{a} + \frac{1}{b} = c$ for $a$ .

Short Answer

Expert verified

The solution for $a$ from the given equation $\frac{1}{a} + \frac{1}{b} = c$ is, $a = \frac{b}{b c - 1}$ .

Step by step solution

01

Step 1. Given information

$\frac{1}{a} + \frac{1}{b} = c$ .

We need to find the solution for $a$ from the given equation.

02

Step 2.Note any value of the variable that would make any denominator zero.

$\frac{1}{a} + \frac{1}{b} = c, a 鈮� 0, b 鈮� 0 .$

Here, the LCD is, $a b$ .

Multiply the given equation with LCD on both sides.

$a b (\frac{1}{a} + \frac{1}{b}) = c . a b$

Distribute the LCD and then simplify it.

$(\frac{a b}{a} + \frac{a b}{b}) = c . a b b + a = a b c$

03

Step 3. Isolate the terms with a.

$b + a = a b c a b c - a = b a (b c - 1) = b a = \frac{b}{b c - 1}$

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Most popular questions from this chapter

In the following exercises, simplify.

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Solve Proportions

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Simplify

In the following exercises, use either method.

$\frac{\frac{2}{r - 9}}{\frac{1}{r + 9} + \frac{3}{r^{2} - 81}}$ .

Efraim wants to start simplifying the complex fraction $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{1}{b}}$ by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim鈥檚 plan.

In the following exercises, solve.

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

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