How do you write the partial fraction decomposition of the rational expression # (4x-1 )/( x^2+3x-4)#?

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Answer 1 · 2018-07-18T06:25:25

The answer is #=(3/5)/(x-1)+(17/5)/(x+4)#

Perform the decomposition into partial fractions

#(4x-1)/(x^2+3x-4)=(4x-1)/((x-1)(x+4))#

#=A/(x-1)+B/(x+4)#

#=(A(x+4)+B(x-1))/((x-1)(x+4))#

The denominators are the same, compare the numerators

#4x-1=A(x+4)+B(x-1)#

Let #x=1#, #=>#, #3=5A#, #=>#, #A=3/5#

Let #x=-4#, #=>#, #-17=-5B#, #=>#, #B=17/5#

Therefore,

#(4x-1)/(x^2+3x-4)=(3/5)/(x-1)+(17/5)/(x+4)#