I have the following inverse laplace transformation:

${L}^{-1}=\frac{s}{(s-3)(s-4)(s-12)}$

After looking at the laplace transformations the closest I've found is:

$\frac{a{e}^{at}-b{e}^{bt}}{a-b}=\frac{s}{(s-a)(s-b)}$

I've been working out a solution for having three variables, but I cant seem to get the correct solution. Is there an identity for this type of transformation?

${L}^{-1}=\frac{s}{(s-3)(s-4)(s-12)}$

After looking at the laplace transformations the closest I've found is:

$\frac{a{e}^{at}-b{e}^{bt}}{a-b}=\frac{s}{(s-a)(s-b)}$

I've been working out a solution for having three variables, but I cant seem to get the correct solution. Is there an identity for this type of transformation?