How do you write the partial fraction decomposition of the rational expression $\frac{x - 16}{x^{2} + x - 2}$ $(x - 16) / (x^2 + x - 2)$ ?

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Answer 1 · 2015-12-13T22:30:44

$\frac{6}{x + 2} - \frac{5}{x - 1}$ $6/(x+2)-5/(x-1)$

The expression equals $\frac{x - 16}{(x + 2) (x - 1)}$ $(x-16)/((x+2)(x-1))$ .

$\frac{x - 16}{(x + 2) (x - 1)} = \frac{A}{x + 2} + \frac{B}{x - 1}$ $(x-16)/((x+2)(x-1))=A/(x+2)+B/(x-1)$

$x - 16 = A (x - 1) + B (x + 2)$ $x-16=A(x-1)+B(x+2)$

IF $x = 1$ $x=1$ :

$- 15 = 3 B$ $-15=3B$
$B = - 5$ $B=-5$

IF $x = - 2$ $x=-2$ :

$- 18 = - 3 A$ $-18=-3A$
$A = 6$ $A=6$

$\frac{x - 16}{x^{2} + x - 2} = \frac{6}{x + 2} - \frac{5}{x - 1}$ $(x-16)/(x^2+x-2)=6/(x+2)-5/(x-1)$

How do you write the partial fraction decomposition of the rational expression x−16x2+x−2(x - 16) / (x^2 + x - 2)?