# Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 80

$\dfrac{x^{2}-2x+73}{(x-4)(x+1)(x+5)}$

#### Work Step by Step

$\dfrac{x+10}{x^{2}-3x-4}-\dfrac{8}{x^{2}+6x+5}-\dfrac{9}{x^{2}+x-20}$ Factor all three fractions completely: $\dfrac{x+10}{(x-4)(x+1)}-\dfrac{8}{(x+5)(x+1)}-\dfrac{9}{(x+5)(x-4)}=...$ Evaluate the indicated operations and simplify: $...=\dfrac{(x+10)(x+5)-8(x-4)-9(x+1)}{(x-4)(x+1)(x+5)}=...$ $...=\dfrac{x^{2}+15x+50-8x+32-9x-9}{(x-4)(x+1)(x+5)}=...$ $...=\dfrac{x^{2}-2x+73}{(x-4)(x+1)(x+5)}$

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