Chapter 4.6, Problem 42E

To determine

To find: The solution of the given equation.

Answer to Problem 42E

The solution of the equation is $\frac{bc}{b-c}$ .

Explanation of Solution

Given:

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

Calculation:

Consider the equation.

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

Solve the given inequality.

  $\begin{array}{c}\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\\ \frac{1}{a}=\frac{1}{c}-\frac{1}{b}\\ =\frac{b-c}{bc}\\ a=\frac{bc}{b-c}\end{array}$

Therefore, the solution of the equation is $\frac{bc}{b-c}$ .