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,

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

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