Question

In the following exercises, perform the indicated operations

$\frac{7m+3}{m+2}-5$

Short answer

Simplified expression is $\frac{2m-7}{m+2}$

Step-by-step solution

Step 1. Given expression   

Expression

$\frac{7m+3}{m+2}-5$

It can be rewritten as

$\frac{7m+3}{m+2}-\frac{5}{1}$

Step 2. Find LCD    

Denominator of the first fraction is $m+2$

Denominator of the second fraction is 1

here nothing is common

So LCD is$\left(m+2\right)\left(1\right)=m+2$

Step 3. Rewrite each rational expression as  an equivalent rational expression with the LCD     

$\frac{7m+3}{m+2}-\frac{5(m+2)}{m+2}$

Step 4.Simplify the numerators.  

$\frac{7m+3}{m+2}-\frac{5m+10}{m+2}$

Step 5. Subtract numerators 

$\frac{(7m+3)-(5m+10)}{m+2}$

Step 6. Simplify numerator 

$$\begin{gathered} \frac{7m+3-5m-10}{m+2} \\ =\frac{2m-7}{m+2} \end{gathered}$$