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Question

v^2+12/v^2-6v-27

Answer 1

Do you want to do partial fraction of (v^2+12)/(v^2-6v-27) ?

Here you go!

(v^2+12)/(v^2-6v-27)

= (v^2-6v-27+6v+27+12)/(v^2-6v-27)

= 1 + (6v+39)/(v^2-6v-27)

= 1 + (6v+39)/[(v-9)(v+3)]

= 1 + A/(v-9) + B/(v+3)

6v+9 = A(v+3) + B(v-9)

Let v = 9, 54+9 = 27A => A = 7/3

Let v = -3, -18+9 = -12B => B = 3/4

Answer: (v^2+12)/(v^2-6v-27) = 1 + (7/3)/(x+3) + (3/4)/(x-9)