Question

How do you express `(2x^2+4x+12)/(x^2+7x+10)` in partial fractions?

Answer 1

`(2x^2+4x+12)/((x+2)(x+5))(x+2)=A/(x+2) *(x+2)+ B/(x+5)(x+2)` Simplify and put in -2 for x, `A = 4`
`(2x^2+4x+12)/((x+2)(x+5))(x+5) = A/(x+2) (x+5)+ B/(x+5)(x+5)` Simplify and put in -5 for x, B= -14
`(2x^2+4x+12)/((x+2)(x+5))=4/(x+2)-14/(x+5)`

Explanation:

To resolve into partial fractions, factor the denominator and split it into fractions. Note that A and B stands for constants. Once you split it up then multiply everything on both sides by x+2, simplify, then put in -2 for x to zero out the other fraction so we can solve for A. Do the same thing for B. Multiply everything on both sides by x+5 and put in -5 to zero out the A so we can solve for B. Once you find the values for A and B then put it into the partial fractions at the beginning.