Decompose the function into partial fractions

(3x + 5) / (x² - 7x + 12)

thank you so much.

(3x+5)/(x²-7x+12) = (3x+5)/((x-3)(x-4)) = A/(x-3) + B/(x-4)
first multiply everything by x-3
so (3x+5)/(x-4) = A + B(x-3)/(x-4)
substitute x with 3
A = -14
similarly by multiplying everything by x-4
and subbing x with 4
B = 17

so (3x + 5) / (x² - 7x + 12) = 17/(x-4) - 14/(x-3)