Partial fraction Problem

**mastermin346** · October 23rd 2011, 11:02 PM

Express $\frac{4x^{4} - 12x^{3} - 12x^{2} + 40}{(x^{2} + 2x + 1)(x - 3)}$

**Prove It** · October 23rd 2011, 11:06 PM

Originally Posted by mastermin346

Express $\frac{4x^{4} - 12x^{3} - 12x^{2} + 40}{(x^{2} + 2x + 1)(x - 3)}$

Start with $\displaystyle \frac{A}{(x + 1)^2} + \frac{B}{x + 1} + \frac{C}{x - 3}$

**Soroban** · November 4th 2011, 06:22 AM

Hello, mastermin346!

$\text{Express: }\:\frac{4x^4 - 12x^3 - 12x^2 + 40}{(x-3)(x+1)^2}$

Long division: . $\frac{4x^4-12x^3-12x^2+40)}{(x-3)(x+1)^2} \;=\;4x - 8 + \frac{-28x + 16}{(x-3)(x+1)^2}$

Then use: . $\frac{-28x+16}{(x-3)(x+1)^2} \;=\;\frac{A}{x-3} + \frac{B}{x+1} + \frac{C}{(x+1)^2}$

And we get: . $A = \text{-}\tfrac{17}{4},\;B = \tfrac{17}{4},\;C = \text{-}11$

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