Chapter 12.5, Problem 45SR

To determine

To solve the equation and state any extraneous solution.

Answer to Problem 45SR

The solution of the equation is $a\text{=8 }$

Extraneous solution of the equation is $a=0,a=2$

Explanation of Solution

Given information:

The given expression is $\frac{4}{a}=\frac{3}{a-2}$

Calculation:

The solution of the expression

  $\begin{array}{l}\frac{4}{a}=\frac{3}{a-2}\\ \frac{4}{a}\left(\frac{a-2}{a-2}\right)=\frac{3}{a-2}\left(\frac{a}{a}\right)\left[\text{write }\frac{4}{a}\text{ and }\frac{3}{a-2}\text{ using LCD,}a\left(a-2\right)\right]\\ \frac{4a-8}{a^2-2a}=\frac{3a}{a^2-2a}\left[\text{simplify}\right]\\ 4a-8=3a\left[\text{multiply both sides by}\left(a^2-2a\right)\right]\\ a-8=0\left[\text{subtract 3}a\text{ from both sides}\right]\\ a\text{=8 }\left[\text{ add 8 to both sides}\right]\end{array}$

Therefore,

Solution of the equation is $a\text{=8 }$

For extraneous solution put denominator of the equation $=0$

  $\begin{array}{l}a=0\\ a-2=0\\ a=2\left[\text{add 2 to both sides}\right]\end{array}$

Therefore,

Extraneous solution of the equation is $a=0,a=2$