How do you express # f(x) = (3x + 2) / [(x - 1)(x + 4)]# in partial fractions?

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Answer 1 · 2016-02-07T12:04:50

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

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

#=> 3x+2 = A(x+4) + B(x-1)#

#=> 3x+2 = (A+B)x +4A-B#

#=>{(A+B=3),(4A-B=2):}#

#=>{(A=1),(B=2):}#

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