Answer
$a=\frac{1}{2},$ and $b=-1$
Work Step by Step
$a+b=ab,$
$\frac{1}{a}-\frac{1}{b}=3,$
$\frac{b-a}{ab}=3,$
$b-a=3ab,$
$b-a=3(a+b),$
$b-a=3a+3b,$
$-2b=4a,$
$a=-\frac{1}{2}b,$
$-\frac{1}{2}b+b=-\frac{1}{2}b(b),$
$\frac{1}{2}b=-\frac{1}{2}b^2,$
$\frac{1}{2}b^2+\frac{1}{2}b=0,$
$\frac{1}{2}b(b+1)=0,$
$b=0$ or $b=-1$
and $a=0$ or $a=\frac{1}{2},$
Therefore, $a=\frac{1}{2},$ and $b=-1$
