Question

How do you write the partial fraction decomposition of the rational expression `(-4x-2)/((x-4)(x-7))`?

Answer 1

`(-4x-2)/((x-4)(x-7))=A/(x-4)+B/(x-7)=A(x-7)+B(x-4)=Ax-7A+Bx-4B`
`-4=A+B,-2=-7A-4B->A=6,B=-10`
`(-4x-2)/((x-4)(x-7))=6/(x-4)-10/(x-7)`

Explanation:

Break up the denominator into two fractions and A and B are constants then multiply by the common denominator and then solve for A and B.