# Chapter R - Algebra Reference - R.3 Rational Expressions - R.3 Exercises: 38

$\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}=\dfrac{5x^{2}+4x-4}{x(x+1)(x-1)}$

#### Work Step by Step

$\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}$ Factor the denominators of all three fractions: $\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}=...$ $...=\dfrac{5x+2}{(x-1)(x+1)}+\dfrac{3}{x(x+1)}-\dfrac{1}{x(x-1)}=...$ Evaluate the indicated operations using the LCD, which is $x(x-1)(x+1)$ in this case: $...=\dfrac{(5x+2)(x)+3(x-1)-(x+1)}{x(x+1)(x-1)}=...$ Simplify: $...=\dfrac{5x^{2}+2x+3x-3-x-1}{x(x+1)(x-1)}=...$ $...=\dfrac{5x^{2}+4x-4}{x(x+1)(x-1)}$

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