Rewrite a function

$f(x)=5+\frac{1}{x+3}$

$f(x)=\frac{5}{1}+\frac{1}{x+3}$

$f(x)=\frac{5\times(x+3)}{1\times(x+3)}+\frac{1}{x+3}$

$f(x)=\frac{5x+15}{x+3}+\frac{1}{x+3}$

$f(x)=\frac{5x+15+1}{x+3}$

$f(x)=\frac{5x+16}{x+3}$

 $f(x) = 5+{1 \over x+3} \\ f(x) = {5(x+3)\over x+3}+{1 \over x+3} \\ f(x) =\frac{5x+16}{x+3} \text{ same as } \frac{ax+b}{x+3}\\ a=5 \\ b=16$