a cheap way to go about it is, let's do away with the denominators, and we'll do so by simply multiplying both sides by the the LCD of all fractions, in this case, that'd be "ab", so we multiply both sides by "ab".
[tex]\bf \cfrac{1}{a}+\cfrac{1}{b}=c\implies\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{ab}}{ab\left( \cfrac{1}{a}+\cfrac{1}{b} \right)=ab(c)}\implies b+a=abc \\\\\\ a=abc-b\implies a=\stackrel{\textit{common factor}}{b(ac-1)}\implies \cfrac{a}{ac-1}=b[/tex]
