How do you write the partial fraction decomposition of the rational expression #(17x-50)/(x^(2)-6x+8)#?

1 Answer
Mar 18, 2018

#(17x-50)/(x^(2)-6x+8) = 8/(x-2)+9/(x-4)#

Explanation:

The denominator #x^2-6x+8# can be factored in the form #(x-2)(x-4)#. So, we try the partial fraction expansion of the form

#(17x-50)/(x^(2)-6x+8) = A/(x-2)+B/(x-4)#

Multiplying both sides by #(x-2)(x-4)# gives us

# 17x - 50 = A(x-4) +B(x-2)#

Now, substituting #x=2# in this equation leads to

#17times 2-50 = Atimes(2-4)+Btimes 0 implies -2A = -16 implies A=8#

and, substituting #x=4# gives

#17times 4-50 = Atimes (4-4)+B times (4-2) implies 2B = 18 implies B = 9#.

Thus

#(17x-50)/(x^(2)-6x+8) = 8/(x-2)+9/(x-4)#