Question
Asked Nov 23, 2019
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How do you complete a partial fraction decomposition? Specifically, when a binomial is over a quadratic?

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Expert Answer

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Step 1

Let an example to understand partial fraction decomposition:

+1
x-
5x 6
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+1 x- 5x 6

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Step 2

If numerator have maximum power equal or more than denominator then numerator is divided

by the denominator before writing its decomposition form.

Partial fraction decomposition formulas:

В
ax +b
A
(х — р)(х — q)
х-р х-д
В
C
ax +b
A
(x-p x-p (x-p)
axbxc
(x-p (x-) x-p (x-p) x-q
(x-p
В
C
A
axbxc
Bx+C
A
(x-p(xqx+r)
x + qx +r
х — р
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В ax +b A (х — р)(х — q) х-р х-д В C ax +b A (x-p x-p (x-p) axbxc (x-p (x-) x-p (x-p) x-q (x-p В C A axbxc Bx+C A (x-p(xqx+r) x + qx +r х — р

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Step 3

Solving the above...

x2-5x6
1
x-5x+6x +
x2-5x6
5x-5
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x2-5x6 1 x-5x+6x + x2-5x6 5x-5

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