Answer
$\frac{13}{14}x+\frac{9}{8}y$
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 all of the fractions) to obtain:
$\frac{3}{7}x+\frac{1}{4}y+\frac{1}{2}x+\frac{7}{8}y$
=$x(\frac{3}{7}+\frac{1}{2})+y(\frac{1}{4}+\frac{7}{8})$
$x(\frac{3}{7}+\frac{1}{2})+y(\frac{1}{4}+\frac{7}{8})$
=$x(\frac{3(2)+7(1)}{14})+y(\frac{1(2)+7(1)}{8})$
=$x(\frac{6+7}{14})+y(\frac{2+7}{8})$
=$x(\frac{13}{14})+y(\frac{9}{8})$
=$\frac{13}{14}x+\frac{9}{8}y$
