Answer
$= \frac{19}{42}$
Work Step by Step
1) First, we plug in the given values, and then we simplify the fractions.
2) Find a common denominator in Step #6: multiply the first fraction by $7$ and the second fraction by $6$ to obtain a common denominator of $42$
$\frac{1}{4}x - \frac{2}{5}y$ for $x = \frac{2}{3}$, $y =-\frac{5}{7} $
$= \frac{1}{4}(\frac{2}{3}) - \frac{2}{5}(-\frac{5}{7})$
$= \frac{1(2)}{4(3)} - \frac{2(-5)}{5(7)}$
$= \frac{2}{12} - \frac{-10}{35}$
$= \frac{2}{12} + \frac{10}{35}$
$= \frac{1}{6} + \frac{2}{7}$
$= \frac{1(7)}{42} + \frac{2(6)}{42}$
$= \frac{7}{42} + \frac{12}{42}$
$= \frac{19}{42}$
