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Write out the form of the partial fraction decomposition of the function. Do not determine the numerical value of the coefficients.

a) $f(x) = \frac{x^2+x}{x^3-3x^2+2x}$

My solution: $$=\frac{x^2+x}{x(x-2)(x-1)} = \frac{A}{x} + \frac{B}{x-2} + \frac{C}{x-1}$$

b) $f(t) = \frac{t^5+1}{t^6+t^3}$

My solution: $$=\frac{t^5+1}{t^3(t^3+1)} = \frac{At^2+Bt+C}{t^3+1} + \frac{D}{t^3}$$

c) $f(x) = \frac{x^5+1}{(x^2-x)(x^4+2x^2+1)}$

My solution: $$=\frac{x^5+1}{x(x-1)(x^2+1)^2} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x} + \frac{F}{x-1}$$

Are they correct?

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    Almost http://www.purplemath.com/modules/partfrac2.htm – 2017-02-11
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    Whats wrong with this?? – 2017-02-12
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    For part b you need $D/t+E/t^2+F/t^3$. @user349557 – 2017-02-12
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    Completely forgot about that, thank you. – 2017-02-12

1 Answers 1

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In part B you need to add a factor over $t^2$ and a factor over $t$.

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    I'm confused, what? – 2017-02-12
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    Look at what you did in part c, with a fraction for each power of a factor of multiplicity 3. Do the same in part b. – 2017-02-12