How do you express # [((3x^2)+3x+12) / ((x-5)(x^2+9))]# in partial fractions?

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Answer 1 · 2016-10-01T01:00:26

#3(x^2 + x + 4)/((x - 5)(x^2 + 9)) = 3 /(x^2+ 9) + 3/(x - 5)#

#3(x^2 + x + 4)/((x - 5)(x^2 + 9)) = (A + Bx)/(x^2+ 9) + C/(x - 5)#

#3(x^2 + x + 4) = (A + Bx)(x - 5) + C(x^2+ 9)#

Let x = 5:

#3(5^2 + 5 + 4) = C(5^2+ 9)#

#C = 3#

Let x = 0:

#3(0^2 + 0 + 4) = (A + B0)(0 - 5) + 3(0^2+ 9)#

#12 = -5A + 27#

#A = 3#

Let x = 1:

#3(1^2 + 1 + 4) = (3 + B)(1 - 5) + 3(1^2+ 9)#

#18 = -12 - 4B + 30#

#B = 0#

#3(x^2 + x + 4)/((x - 5)(x^2 + 9)) = 3 /(x^2+ 9) + 3/(x - 5)#