Simplify: $ \frac{11}{2} x^{2} y-\frac{9}{4} x y^{2}+\frac{1}{4} x y-\frac{1}{14} y^{2} x+\frac{1}{15} y x^{2}+\frac{1}{2} x y $.
Given:
\( \frac{11}{2} x^{2} y-\frac{9}{4} x y^{2}+\frac{1}{4} x y-\frac{1}{14} y^{2} x+\frac{1}{15} y x^{2}+\frac{1}{2} x y \).
To do:
We have to simplify the given expression.
Solution:
We know that like terms can be added and subtracted in an expression.
Therefore,
$\frac{11}{2} x^{2} y-\frac{9}{4} x y^{2}+\frac{1}{4} x y-\frac{1}{14} y^{2} x+\frac{1}{15} y x^{2}+\frac{1}{2} x y=(\frac{11}{2}+\frac{1}{15})x^2y-(\frac{9}{4}+\frac{1}{14})xy^2+(\frac{1}{4}+\frac{1}{2})xy$
$=\left(\frac{11\times 15+1\times 2}{30}\right) x^{2} y-\left(\frac{9\times 7+1\times 2}{28}\right) xy^{2} +\left(\frac{1+1\times 2}{4}\right) xy$
$=\left(\frac{165+2}{30}\right) x^{2} y-\left(\frac{63+2}{28}\right) xy^{2} +\left(\frac{1+2}{4}\right) xy$
$=\frac{167}{30} x^{2} y-\frac{65}{28} xy^{2} +\frac{3}{4} xy$.
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