# Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 54

$\displaystyle \frac{x^{4}+x^{3}-x^{2}+x-1}{x^{3}(x^{2}+1)}$

#### Work Step by Step

Both denominators are irreducible. LCD = $x^{3}(x^{2}+1)$ $\displaystyle \frac{x-1}{x^{3}}+\frac{x}{x^{2}+1}=\frac{(x-1)(x^{2}+1)+x\cdot x^{3}}{x^{3}(x^{2}+1)}$ $=\displaystyle \frac{(x^{3}+x-x^{2}-1)+x^{4}}{x^{3}(x^{2}+1)}$ $=\displaystyle \frac{(x^{3}+x-x^{2}-1)+x^{4}}{x^{3}(x^{2}+1)}$ $=\displaystyle \frac{x^{4}+x^{3}-x^{2}+x-1}{x^{3}(x^{2}+1)}$

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