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

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Answer 1 · 2015-12-29T08:19:11

$\frac{2}{x (4 x - 1)} = \frac{8}{4 x - 1} - \frac{2}{x}$ $2/(x(4x-1))=8/(4x-1)-2/x$

Split into parts.

$\frac{2}{x (4 x - 1)} = \frac{A}{x} + \frac{B}{4 x - 1}$ $2/(x(4x-1))=A/x+B/(4x-1)$

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

$2 = A (4 x - 1) + B x$ $2=A(4x-1)+Bx$

Plug in $\frac{1}{4}$ $1/4$ for $x$ $x$ .

$2 = \frac{1}{4} B$ $2=1/4B$

$B = 8$ $B=8$

Plug in $0$ $0$ for $x$ $x$ .

$2 = - A$ $2=-A$

$A = - 2$ $A=-2$

Thus,

$\frac{2}{x (4 x - 1)} = \frac{8}{4 x - 1} - \frac{2}{x}$ $2/(x(4x-1))=8/(4x-1)-2/x$

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