MHB Partial fraction decomposition

[Jordan1994]

Q3.) Express as partial fractions.

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

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

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

 

[MarkFL]

Let's begin with a). Can you state the form the partial fraction will take?

 

[Krizalid1]

Here's a) without the full method:

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