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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.83 (page 693)

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

Short Answer

Expert verified

The solution is $a = \frac{b}{(b c - 1)}$ .

Step by step solution

01

Step 1. Given

The given equation is: $\frac{1}{a} + \frac{1}{b} = c$ .

02

Step 2. To find

We have to solve the equation for a.

03

Step 3. Calculation

We will solve this problem using LCD.

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

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Most popular questions from this chapter

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

Simplify the complex rational expression by using the LCD:

$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Danica can sail her boat 5 miles into a 7 mph headwind in the same amount of time she can sail 12 miles with a 7 mph tailwind. What is the speed of Danica’s boat without a wind?

In the following exercise, find

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

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

$f (x) = \frac{6 x}{x^{2} - 64} g (x) = \frac{3}{x - 8}$

Simplify the complex rational expression by writing it as division:

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

See all solutions

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