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Question
Add the following algebraic expression:
\[\frac{11}{2}xy + \frac{12}{5}y + \frac{13}{7}x, - \frac{11}{2}y - \frac{12}{5}x - \frac{13}{7}xy\]
Solution
To add, we proceed as follows:
\[\left( \frac{11}{2}xy + \frac{12}{5}y + \frac{13}{7}x \right) + \left( - \frac{11}{2}y - \frac{12}{5}x - \frac{13}{7}xy \right)\]
\[ = \frac{11}{2}xy + \frac{12}{5}y + \frac{13}{7}x - \frac{11}{2}y - \frac{12}{5}x - \frac{13}{7}xy\]
\[ = \frac{11}{2}xy - \frac{13}{7}xy + \frac{12}{5}y - \frac{11}{2}y + \frac{13}{7}x - \frac{12}{5}x ( \text { Collecting like terms })\]
\[ = \frac{51}{14}xy - \frac{31}{10}y - \frac{19}{35}x (\text { Combining like terms })\]
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