For Exercise, solve the equation. 48m2−4m+3=12m−4

Step 1
We factor the denominators
${\displaystyle \frac{48}{m^2-4m}+3=\frac{12}{m-4}}$
${\displaystyle \frac{48}{m(m-4)}+3=\frac{12}{m-4}}$
LCD is ${\displaystyle m(m-4)}$
Then we multiply both sides by LCD so that we get rid of the fractions
${\displaystyle \frac{48}{m(m-4)}+3=\frac{12}{m-4}}$
${\displaystyle m(m-4)[\frac{48}{m(m-4)}+3]=m(m-4)\frac{12}{m-4}}$
${\displaystyle 48+3m(m-4)=12m}$
Step 2
Then distribute 3m, combine the like terms and then make right side equal to 0.
Then factor
${\displaystyle 48+3m(m-4)=12m}$
${\displaystyle 48+3m^2-12m=12m}$
${\displaystyle 3m^2-24m+48=0}$
${\displaystyle 3(m^2-8m+16)=0}$
${\displaystyle 3(m-4)(m-4)=0}$
${\displaystyle 3{(m-4)}^2=0}$
Set each factor equal to 0 and solve for m
${\displaystyle m-4=0}$
${\displaystyle m=4}$
For ${\displaystyle m=4}$ we get denominator equal to 0 in the original equation. So ${\displaystyle m=4}$ can not be a solution
Answer: No solution