Express (16x+78)/(2x^2+25x+63) as two fractions

Firstly factorise the denominator to get (2x+7)(x+9). Then make the fraction equal to the seperate fractions with constants.

E.g 16x+78/2x^2+25x+63=A/(2x+7)+B/(x+9). then multiply accross by the denominator to get 16x+78=A(x+9)+B(2x+7)

the subtitute in x to make one term equal 0. e.g x=-9.to get -66=-11B therefor B=-6. then substitue in x=-7/2 to get 22=(11/2)B therfore B=4

so the answer is 4/(2x+7)+6/(x+9)