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Question
Subtract:
\[\frac{3}{2}x - \frac{5}{4}y - \frac{7}{2}z \text { from }\frac{2}{3}x + \frac{3}{2}y - \frac{4}{3}z\]
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Solution
\[\left( \frac{2}{3}x + \frac{3}{2}y - \frac{4}{3}z \right) - \left( \frac{3}{2}x - \frac{5}{4}y - \frac{7}{2}z \right)\]
\[ = \frac{2}{3}x + \frac{3}{2}y - \frac{4}{3}z - \frac{3}{2}x + \frac{5}{4}y + \frac{7}{2}z\]
\[ = \frac{2}{3}x - \frac{3}{2}x + \frac{3}{2}y + \frac{5}{4}y - \frac{4}{3}z + \frac{7}{2}z (\text { Collecting like terms } )\]
\[ = - \frac{5}{6}x + \frac{11}{4}y + \frac{13}{6}z (\text { Combining like terms })\]
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