Chapter 4.6, Problem 37E

To determine

To find: The rational equation to that cannot have the given solutions.

Answer to Problem 37E

The rational equation to that cannot have the given solutions is $\frac{-1}{30}$ .

Explanation of Solution

Given:

The rational equation cannot have $3$ and $-2$ as a solution.

Calculation:

Suppose the rational equation is $\frac{1}{5}+\frac{1}{x}=\frac{1}{6}$ .

Solve the equation $\frac{1}{5}+\frac{1}{x}=\frac{1}{6}$ .

  $\begin{array}{c}\frac{1}{5}+\frac{1}{x}=\frac{1}{6}\\ \frac{1}{x}=\frac{1}{6}-\frac{1}{5}\\ =\frac{5-6}{30}\\ =\frac{-1}{30}\end{array}$

Therefore, therational equation to that cannot have the given solutions is $\frac{-1}{30}$ .