Chapter 5.9, Problem 4WE

To determine

To solve: the given equation for $\mathrm{u}$ . Check the result.

Answer to Problem 4WE

The value of $\mathrm{u}$ in the given equation is $4$ .

Explanation of Solution

Given information:

Given equation is

  $\frac{3}{\mathrm{u}+2}=\frac{1}{\mathrm{u}-2}$

Calculation:

Consider the given equation,

  $\frac{3}{\mathrm{u}+2}=\frac{1}{\mathrm{u}-2}$

Now, solve the equation as shown,

  $\begin{array}{c}\frac{3}{\mathrm{u}+2}=\frac{1}{\mathrm{u}-2}\\ 3\mathrm{u}-6=\mathrm{u}+2\\ 3\mathrm{u}-\mathrm{u}=6+2\\ 2\mathrm{u}=8\\ \mathrm{u}=4\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\frac{3}{\mathrm{u}+2}=\frac{1}{\mathrm{u}-2}\\ \frac{3}{4+2}=\frac{1}{4-2}\\ \frac{3}{6}=\frac{1}{2}\\ \frac{1}{2}=\frac{1}{2}\end{array}$

Which is true.

Hence, the value of $\mathrm{u}$ in the given equation is $4$ .