Partial Fraction Decomposition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Decompose 3x+5(x+1)(x+2)\dfrac{3x+5}{(x+1)(x+2)}.

Solution

  1. 1
    A/(x+1)+B/(x+2)A/(x+1)+B/(x+2). x=−1x=-1: A=2A=2. x=−2x=-2: B=1B=1.

Answer

2x+1+1x+2\frac{2}{x+1} + \frac{1}{x+2}
Use strategic substitution at each root of the denominator.

About Partial Fraction Decomposition

Breaking a rational expression into a sum of simpler fractions whose denominators are the factors of the original denominator.

Learn more about Partial Fraction Decomposition →

More Partial Fraction Decomposition Examples

Example 1 easy

Decompose [formula] and integrate.

Example 2 hard

Integrate [formula].

Example 4 medium

Integrate [formula].

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