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#### Jordan1994

##### New member

- Feb 2, 2014

- 4

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

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

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

- Thread starter Jordan1994
- Start date

- Thread starter
- #1

- Feb 2, 2014

- 4

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

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

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

- Admin
- #2

- Feb 9, 2012

- 118

\(\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*}\)