Based on this thread:
This is the correct form:
\(\displaystyle \dfrac{5x^2+23x+24}{(2x+3)(x+2)^2}=\dfrac{A}{2x+3} + \dfrac{B}{x+2} + \dfrac{C}{(x+2)^2} \)
Your link shows an example that is similar enough for that step.
Because of the 2 exponent in the denominator [the (x+2)2] you will need three terms
\(\displaystyle \dfrac{5x^2+23x+24}{(2x+3)(x+2)^2}=\dfrac{A}{2x+3} + \dfrac{B}{x+2} + \dfrac{Cx+D}{(x+2)^2} \ \ \ \ \ \) <------ That's not the correct form.
You might want to look at
http://www.mathsisfun.com/algebra/partial-fractions.html
This is the correct form:
\(\displaystyle \dfrac{5x^2+23x+24}{(2x+3)(x+2)^2}=\dfrac{A}{2x+3} + \dfrac{B}{x+2} + \dfrac{C}{(x+2)^2} \)
Your link shows an example that is similar enough for that step.
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