Question

In the following exercises, solve.

$\frac{5}{2}-\frac{1}{c}=\frac{3}{4}$

Short answer

The solution of the equation$\frac{5}{2}-\frac{1}{c}=\frac{3}{4}$is

$c=\frac{4}{7}$

Step-by-step solution

Step 1. Given information

The given equation is

$\frac{5}{2}-\frac{1}{c}=\frac{3}{4}$

Step 2. Solution of equation 

In the equation, the term $\frac{1}{c}$is undefined for$c=0$

sorole="math" localid="1647783729429" $\frac{5}{2}-\frac{1}{c}=\frac{3}{4},c\ne 0$

the least common denominator of all denominators in the equation is$4c$

multiply both sides of the equation by the least common denominator$4c$

$$\begin{gathered} 4c\left(\frac{5}{2}-\frac{1}{c}\right)=4c\left(\frac{3}{4}\right) \\ 4c\left(\frac{5}{2}\right)-4c\left(\frac{1}{c}\right)=4c\left(\frac{3}{4}\right) \\ 10c-4=3c \\ 7c=4 \\ c=\frac{4}{7} \end{gathered}$$

So the solution of the equation is$\frac{4}{7}$

Step 3. Verification 

Substitute $c=\frac{4}{7}$in the equation

$$\begin{gathered} \frac{5}{2}-\frac{1}{c}=\frac{3}{4} \\ \frac{5}{2}-\frac{1}{\frac{4}{7}}\stackrel{?}{=}\frac{3}{4} \\ \frac{10}{4}-\frac{7}{4}\stackrel{?}{=}\frac{3}{4} \\ \frac{3}{4}=\frac{3}{4} \end{gathered}$$

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