Answer
$= \frac{1}{17}$
Work Step by Step
1. Follow the acronym PEDMAS:
P: arenthesis
E: ponents
D:ivision
M:ultiplication
A:ddition
S:ubtraction
$= $ P.E.D.M.A.S
This is used to determine which order of operations is completed first from top to bottom. For example, you would complete the division of two numbers before the addition of another two numbers. In this case, we multiply before subtracting and adding:
$\frac{3}{5}x - \frac{1}{3}x + \frac{7}{15}x - \frac{2}{3}x$ for $x = \frac{15}{17}$
$= \frac{3}{5}(\frac{15}{17}) - \frac{1}{3}(\frac{15}{17}) + \frac{7}{15}(\frac{15}{17}) - \frac{2}{3}(\frac{15}{17})$
$= \frac{45}{85} - \frac{15}{51} + \frac{105}{255} - \frac{30}{51}$
2. Simplify the fractions
$= \frac{9}{17} - \frac{5}{17} + \frac{21}{51} - \frac{10}{17}$
$= \frac{9}{17} - \frac{5}{17} - \frac{10}{17} + \frac{21}{51}$
$= \frac{-6}{17} + \frac{21}{51}$
3. Find a common denominator: multiply the first fraction by $51/51$ and the second fraction by $17/17$
$= \frac{-6(51)}{867} + \frac{21(17)}{867}$
$= \frac{-306}{867} + \frac{357}{867}$
$= \frac{51}{867}$
$= \frac{3}{51}$
$= \frac{1}{17}$
