How do you write the partial fraction decomposition of the rational expression $\frac{7}{x^{2} - 14 x}$ $7/(x^2-14x)$ ?

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Answer 1 · 2015-12-24T05:37:30

$\frac{7}{x^{2} - 14 x} = - \frac{1}{2 x} + \frac{1}{2 (x - 14)}$ $7/(x^2-14x)=-1/(2x)+1/(2(x-14))$

Factor and then break up the denominator.

$\frac{7}{x (x - 14)} = \frac{A}{x} + \frac{B}{x - 14}$ $7/(x(x-14))=A/x+B/(x-14)$

Find a common denominator of $x (x - 14)$ $x(x-14)$ .

$7 = A (x - 14) + B x$ $7=A(x-14)+Bx$

Plug in $0$ $0$ for $x$ $x$ :

$7 = - 14 A$ $7=-14A$
$A = - \frac{1}{2}$ $A=-1/2$

Plug in $14$ $14$ for $x$ $x$ :

$7 = 14 B$ $7=14B$
$B = \frac{1}{2}$ $B=1/2$

Plug these values into the original expression.

$\frac{7}{x^{2} - 14 x} = - \frac{1}{2 x} + \frac{1}{2 (x - 14)}$ $7/(x^2-14x)=-1/(2x)+1/(2(x-14))$

How do you write the partial fraction decomposition of the rational expression 7x2−14x7/(x^2-14x)?