How do you express #(x^3 - 5x + 2) / (x^2 - 8x + 15)# in partial fractions?
1 Answer
Aug 7, 2016
Explanation:
#(x^3-5x+2)/(x^2-8x+15)#
#=(x^3-8x^2+15x+8x^2-64x+120+44x-118)/(x^2-8x+15)#
#=(x(x^2-8x+15)+8(x^2-8x+15)+44x-118)/(x^2-8x+15)#
#=x+8+(44x-118)/(x^2-8x+15)#
#=x+8+(44x-118)/((x-3)(x-5))#
#=x+8+A/(x-3)+B/(x-5)#
Using Heaviside's cover-up method, we find:
#A=(44(3)-118)/((3)-5) = (132-118)/(-2) = 14/(-2) = -7#
#B=(44(5)-118)/((5)-3) = (220-118)/2 = 102/2 = 51#
So:
#(x^3-5x+2)/(x^2-8x+15) = x+8-7/(x-3)+51/(x-5)#
