Answer
$-\frac{11}{45}x-\frac{9}{20}y$
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:
$\frac{2}{9}x+\frac{5}{12}y-\frac{7}{15}x-\frac{13}{15}y$
=$x(\frac{2}{9}-\frac{7}{15})+y(\frac{5}{12}-\frac{13}{15})$
=$x(\frac{2(5)-7(3)}{45})+y(\frac{5(5)-13(4)}{60})$
=$x(\frac{10-21}{45})+y(\frac{25-52}{60})$
=$x(\frac{-11}{45})+y(\frac{-27}{60})$
=$-\frac{11}{45}x-\frac{9}{20}y$
