How do you write the partial fraction decomposition of the rational expression $x/((x+7)(x+8)(x+9))$ ?

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Answer 1 · 2016-08-07T23:02:00

$x/((x+7)(x+8)(x+9)) = -7/(2(x+7))+8/(x+8)-9/(2(x+9))$

$x/((x+7)(x+8)(x+9)) = A/(x+7)+B/(x+8)+C/(x+9)$

Using Heaviside's cover-up method, we find:

$A = (-7)/(((-7)+8)((-7)+9)) = (-7)/2 = -7/2$

$B = (-8)/(((-8)+7)((-8)+9)) = (-8)/(-1) = 8$

$C = (-9)/(((-9)+7)((-9)+8)) = (-9)/2 = -9/2$

So:

$x/((x+7)(x+8)(x+9)) = -7/(2(x+7))+8/(x+8)-9/(2(x+9))$

How do you write the partial fraction decomposition of the rational expression x/((x+7)(x+8)(x+9)) x/((x+7)(x+8)(x+9))?