Chapter 7.4, Problem 8WE

To determine

To solve: the expression as mentioned in the problem.

Answer to Problem 8WE

The solution exist and it is $a=1$ .

Explanation of Solution

Given information:

The expression is $\frac{3}{2a}-\frac{5}{6}=\frac{2}{3a}$ .

Formula used:

We will use L.C.M of the denominator.

We will use cross multiplication method.

Calculation:

Consider the expression $\frac{3}{2a}-\frac{5}{6}=\frac{2}{3a}$ .

Here variable is $a$ in the mentioned expression above.

Recall that we will take the L.C.M of the denominator.

Therefore L.C.M of $\left(2a,6\right)$ is $6a$ .

Therefore $\frac{3}{2a}-\frac{5}{6}=\frac{2}{3a}\Rightarrow \frac{3*3-5*a}{6a}=\frac{2}{3a}\Rightarrow \frac{9-5a}{6a}=\frac{2}{3a}$ .

Recall that we will use cross multiplication method.

  $\frac{9-5a}{6a}=\frac{2}{3a}\Rightarrow 3a*\left(9-5a\right)=2*6a\Rightarrow 9-5a=4\Rightarrow 9-4=5a\Rightarrow 5a=5\Rightarrow a=1$ .

Therefore the solution exist and it is $a=1$ .