Partial fractions

Algebra Skills (Lesson 1/2)

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Linear partial fractions

When the denominator of a fraction can be factored, it is possible to split it into the sum of 2 pieces:

x2+2x−34x−8≡(x+3)(x−1)4x−8

(where ≡ means "equal for all x")

Remember that when we add two fractions, we cross multiply the denominators:

x+3A+x−1B≡(x+3)(x−1)A(x−1)+B(x+3)

Then we can write

4x−8≡A(x−1)+B(x+3)

The easiest way to solve this is to chose a value of x that eliminates A or B, eg x=1:

4⋅1−8=A⋅(1−1)+B(1+3)

−4=4B⇒B=−1

and therefore

4x−8=Ax−A−x−3⇒A=5