Chapter 5.9, Problem 6WE

To determine

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

Answer to Problem 6WE

The value of $\mathrm{r}$ in the given equation is $9$ .

Explanation of Solution

Given information:

Given equation is

  $\frac{5}{2\mathrm{r}+1}-\frac{3}{2\mathrm{r}-1}=0$

Calculation:

Consider the given equation,

  $\frac{5}{2\mathrm{r}+1}-\frac{3}{2\mathrm{r}-1}=0$

Now, solve the equation as shown,

  $\begin{array}{c}\frac{5}{2\mathrm{r}+1}-\frac{3}{2\mathrm{r}-1}=0\\ \frac{5}{2\mathrm{r}+1}=\frac{3}{2\mathrm{r}-1}\\ 10\mathrm{r}-5=6\mathrm{r}+3\\ 10\mathrm{r}-6\mathrm{r}=5+3\\ 4\mathrm{r}=8\\ \mathrm{r}=2\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\frac{5}{2\mathrm{r}+1}-\frac{3}{2\mathrm{r}-1}=0\\ \frac{5}{2\left(2\right)+1}-\frac{3}{2\left(2\right)-1}=0\\ \frac{5}{5}-\frac{3}{3}=0\\ 1-1=0\\ 0=0\end{array}$

Which is true.

Hence, the value of $\mathrm{r}$ in the given equation is $2$ .