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

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Answer 1 · 2015-12-29T08:19:11

#2/(x(4x-1))=8/(4x-1)-2/x#

Split into parts.

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

Multiply for a common denominator of #x(4x-1)#.

#2=A(4x-1)+Bx#

Plug in #1/4# for #x#.

#2=1/4B#

#B=8#

Plug in #0# for #x#.

#2=-A#

#A=-2#

Thus,

#2/(x(4x-1))=8/(4x-1)-2/x#