Writing partial fraction decomposition for $f(x) = \frac{7}{x^5 + 2x^3 + x}$ (without evaluating the constants), we obtain $\frac{A}{x} + \frac{B}{x^2} + \frac{Cx + D}{x^2 + 1} + \frac{Ex + F}{(x^2 + 1)^2}$ This option $\frac{A}{x} + \frac{Bx + C}{(x^2 + 1)^2}$ $\frac{A}{x} + \frac{B}{x^2} + \frac{C}{x^3} + \frac{Dx + E}{x^2 + 1}$ This option $\frac{A}{x} + \frac{Bx + C}{x^2 + 1} + \frac{Dx + E}{(x^2 + 1)^2}$
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The denominator is r^2 + 1, which cannot be factored further since it is a sum of squares. Show more…
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Write out the form of the partial fraction decomposition of the function frac{x^3 + x^2 + 1}{x(x - 1)(x^2 + x + 1)(x^2 + 1)^3} SOLUTION frac{x^3 + x^2 + 1}{x(x - 1)(x^2 + x + 1)(x^2 + 1)^3} = frac{A}{x} + frac{B}{x - 1} + frac{Cx + D}{x^2 + x + 1} + frac{Ex + F}{x^2 + 1} + frac{Gx + H}{(x^2 + 1)^2} + frac{Ix + J}{(x^2 + 1)^3}
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