Question

In the following exercises, solve.

$\frac{5}{6}+\frac{3}{b}=\frac{1}{3}$

Short answer

The solution of the equation$\frac{5}{6}+\frac{3}{b}=\frac{1}{3}$is

$x=-6$

Step-by-step solution

Step 1. Given information

The given equation is

$\frac{5}{6}+\frac{3}{b}=\frac{1}{3}$

Step 2. Solution of equation

In the equation, the term $\frac{3}{b}$is undefined if $b=0$

so role="math" localid="1647782581521" $\frac{5}{6}+\frac{3}{b}=\frac{1}{3},b\ne 0$

the least common denominator of all denominators in the equation is $6b$

multiply both sides of the equation by the least common denominator $6b$

$$\begin{gathered} 6b\left(\frac{5}{6}+\frac{3}{b}\right)=6b\left(\frac{1}{3}\right) \\ 6b\left(\frac{5}{6}\right)+6b\left(\frac{3}{b}\right)=\frac{6b}{3} \\ 5b+18=2b \\ 3b=-18 \\ b=-6 \end{gathered}$$

So the solution of the equation is$b=-6$

Step 3. Verification

Substitute $x=2$in the equation

$$\begin{gathered} \frac{5}{6}+\frac{3}{b}=\frac{1}{3} \\ \frac{5}{6}+\frac{3}{-6}\stackrel{?}{=}\frac{1}{3} \\ \frac{5-3}{6}\stackrel{?}{=}\frac{1}{3} \\ \frac{2}{6}\stackrel{?}{=}\frac{1}{3} \\ \frac{1}{3}=\frac{1}{3} \end{gathered}$$

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