## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{3}{2}$
$\bf{\text{Solution Outline:}}$ Use the $LCD$ to convert the terms of the given expression, $\dfrac{2}{3}+\dfrac{5}{6} ,$ to similar terms. Once expressed as similar terms, operate on the numerators and copy the common denominator. $\bf{\text{Solution Details:}}$ The prime factorization of $3$ is $3=3^1.$ The prime factorization of $6$ is $6=2^1\cdot3^1.$ Getting each factor with the highest exponent, then the $LCD=2^1\cdot3^1=6 .$ Converting the terms of the given expression to similar terms by using the $LCD$ results to \begin{array}{l}\require{cancel} \dfrac{2}{3}\cdot\dfrac{2}{2}+\dfrac{5}{6} \\\\= \dfrac{4}{6}+\dfrac{5}{6} \\\\= \dfrac{4+5}{6} \\\\= \dfrac{9}{6} \\\\= \dfrac{\cancel3(3)}{\cancel3(2)} \\\\= \dfrac{3}{2} .\end{array}