Chapter 8.6, Problem 2CGP

To determine

To solve the given equation.

Answer to Problem 2CGP

  $v=\frac{13}{24}$

Explanation of Solution

Given:

The given equation is

  $\frac{4}{8v-3}-\frac{3}{8v-2}=\frac{4}{8v+3}$

Calculation:

Solving the equation as follows-

  $\begin{array}{l}\frac{4}{8v-3}-\frac{3}{8v-2}=\frac{4}{8v-2}\\ \Rightarrow \frac{4(8v-2)-3(8v-3)}{\left(8v-3\right)(8v-2)}=\frac{4}{8v-2}\\ \Rightarrow \frac{32v-8-24v+9}{\left(8v-3\right)(8v-2)}=\frac{4}{8v-2}\\ \Rightarrow 8v+1=4(8v-3)\\ \Rightarrow 8v+1=32v-12\\ \Rightarrow 32v-8v=13\\ \Rightarrow 24v=13\\ \Rightarrow v=\frac{13}{24}\end{array}$

The solution is $v=\frac{13}{24}$