Answer
$\frac{23}{18}x+\frac{29}{20}y$
Work Step by Step
We first factor out $x$ and $y$. Then, to simplify this expression, we find the common denominator (which is the LCM of the denominators of the fractions) to obtain:
$\frac{5}{6}x+\frac{3}{4}y+\frac{4}{9}x+\frac{7}{10}y$
=$x(\frac{5}{6}+\frac{4}{9})+y(\frac{3}{4}+\frac{7}{10})$
=$x(\frac{5(3)+4(2)}{18})+y(\frac{3(5)+7(2)}{20})$
=$x(\frac{15+8}{18})+y(\frac{15+14}{20})$
=$x(\frac{23}{18})+y(\frac{29}{20})$
=$\frac{23}{18}x+\frac{29}{20}y$
