Question

In the following exercises, solve.

$\frac{6}{3}-\frac{2}{d}=\frac{4}{9}$

Short answer

The solution of the equation$\frac{6}{3}-\frac{2}{d}=\frac{4}{9}$is

$d=\frac{9}{7}$

Step-by-step solution

Step 1. Given information

The given equation is

$\frac{6}{3}-\frac{2}{d}=\frac{4}{9}$

Step 2. Solution of equation 

In the equation, the term $\frac{2}{d}$is undefined for$d=0$

sorole="math" localid="1647784110699" $\frac{6}{3}-\frac{2}{d}=\frac{4}{9},d\ne 0$

the least common denominator of all denominators in the equation is$9d$

multiply both sides of the equation by the least common denominator$9d$

$$\begin{gathered} 9d\left(\frac{6}{3}-\frac{2}{d}\right)=9d\left(\frac{4}{9}\right) \\ 9d\left(\frac{6}{3}\right)-9d\left(\frac{2}{d}\right)=9d\left(\frac{4}{9}\right) \\ 18d-18=4d \\ 14d=18 \\ d=\frac{18}{14} \\ d=\frac{9}{7} \end{gathered}$$

So the solution of the equation is$d=\frac{9}{7}$

Step 3. Verification 

Substitute $d=\frac{9}{7}$in the equation

$$\begin{gathered} \frac{6}{3}-\frac{2}{d}=\frac{4}{9} \\ \frac{6}{3}-\frac{2}{\frac{9}{7}}\stackrel{?}{=}\frac{4}{9} \\ \frac{18}{9}-\frac{14}{9}\stackrel{?}{=}\frac{4}{9} \\ \frac{4}{9}=\frac{4}{9} \end{gathered}$$

The left-hand side is equal to the right-hand side so the solution is correct.