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Question
Take away:
\[\frac{2}{3}ac - \frac{5}{7}ab + \frac{2}{3}bc\text { from } \frac{3}{2}ab - \frac{7}{4}ac - \frac{5}{6}bc\]
Solution
The difference is given by:
\[\left( \frac{3}{2}ab - \frac{7}{4}ac - \frac{5}{6}bc \right) - \left( \frac{2}{3}ac - \frac{5}{7}ab + \frac{2}{3}bc \right)\]
\[ = \frac{3}{2}ab-\frac{7}{4}ac-\frac{5}{6}bc-\frac{2}{3}ac+\frac{5}{7}ab-\frac{2}{3}bc\]
\[= \frac{3}{2}ab + \frac{5}{7}ab - \frac{7}{4}ac - \frac{2}{3}ac - \frac{5}{6}bc - \frac{2}{3}bc\] (Collecting like terms )
= \[\left( \frac{21 + 10}{14} \right)ab + \left( \frac{- 21 - 8}{12} \right)ac + \left( \frac{- 5 - 4}{6} \right)bc\]
\[=\frac{31}{14}ab-\frac{29}{12}ac-\frac{3}{2}bc\] (Combining like terms )
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