# How do you simplify 1/3x+2/7x-3/4y-1/2y?

Nov 21, 2016

simplified form

• $\frac{20}{21} x - \frac{5}{4} y$

#### Explanation:

goal: simplify the equation to have only two terms

calculations:
split up $x$ terms and $y$ terms; simplify separately

set the denominators of all terms with variable $x$ equal, and simplify
$\frac{1}{3} x + \frac{2}{7} x \setminus \Rightarrow \frac{1}{3} x \left(\frac{7}{7}\right) + \frac{2}{7} x \left(\frac{3}{3}\right) = \frac{14}{21} x + \frac{6}{21} x = \frac{20}{21} x$
set the denominators of all terms with variable $y$ equal, and simplify
$- \frac{3}{4} y - \frac{1}{2} y \setminus \Rightarrow - \frac{3}{4} y - \frac{1}{2} y \left(\frac{2}{2}\right) = - \frac{3}{4} y - \frac{2}{4} y = - \frac{5}{4} y$

combine the previously simplified forms
$\frac{20}{21} x - \frac{5}{4} y$