# Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set: 66

$\dfrac{34-9x}{15x-30}$

#### Work Step by Step

Factoring the given expression, $\dfrac{5}{3x-6}-\dfrac{x}{x-2}+\dfrac{3+2x}{5x-10} ,$ results to \begin{array}{l}\require{cancel} \dfrac{5}{3(x-2)}-\dfrac{x}{x-2}+\dfrac{3+2x}{5(x-2)} .\end{array} Using the $LCD= 15(x-2)$, the expression above simplifies to \begin{array}{l} \dfrac{5(5)-15(x)+3(3+2x)}{15(x-2)} \\\\= \dfrac{25-15x+9+6x}{15(x-2)} \\\\= \dfrac{34-9x}{15(x-2)} \\\\= \dfrac{34-9x}{15x-30} .\end{array}

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