Take away:
$ \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x $ from $ \frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4} $

Given:

Given expressions are \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) and \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4} \).
To do:
 We have to take away \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4} \).

Solution:

$(\frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4})-(\frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x)=(\frac{1}{3}+\frac{4}{5})x^3+(-\frac{5}{2}-\frac{6}{5})x^2+(\frac{3}{5}-\frac{3}{2})x+(\frac{1}{4}-\frac{5}{6})$

$=\frac{5+12}{15}x^3-\frac{25+12}{10}x^2+\frac{6-15}{10}x+\frac{3-10}{12}$

$=\frac{17}{15}x^3-\frac{37}{10}x^2-\frac{9}{10}x-\frac{7}{12}$