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Partial fraction decomposition

Jordan1994

New member
Feb 2, 2014
4
Q3.) Express as partial fractions.

a) \(\displaystyle \frac{3x+4}{x^2+3x+2}\)

b) \(\displaystyle \frac{5x^2+5x+8}{(x+2)\left(x^2+2 \right)}\)

c) \(\displaystyle \frac{x^2+15x+21}{(x+2)^2(x-3)}\)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Let's begin with a). Can you state the form the partial fraction will take?
 

Krizalid

Active member
Feb 9, 2012
118
Here's a) without the full method:

\(\displaystyle \begin{align*}
\frac{3x+4}{{{x}^{2}}+3x+2}&=\frac{3x+4}{(x+1)(x+2)} \\
& =\frac{2x+2+x+2}{(x+1)(x+2)} \\
& =\frac{2(x+1)+x+2}{(x+1)(x+2)} \\
& =\frac{2}{x+2}+\frac{1}{x+1}. \\
\end{align*}\)