Answer
$\frac{x^{2}}{3}-x+1$
Work Step by Step
We are given the expression $(\frac{2x^{2}}{3}-\frac{x}{6}+\frac{5}{6})-(\frac{x^{2}}{3}+\frac{5x}{6}-\frac{1}{6})$. We can subtract the second polynomial from the first polynomial by adding the opposite of the second polynomial to the first polynomial.
$(\frac{2x^{2}}{3}-\frac{x}{6}+\frac{5}{6})+(-\frac{x^{2}}{3}-\frac{5x}{6}+\frac{1}{6})$
We can combine like terms to simplify.
$(\frac{2x^{2}}{3}-\frac{x^{2}}{3})+(-\frac{x}{6}-\frac{5x}{6})+(\frac{5}{6}+\frac{1}{6})=\frac{x^{2}}{3}-\frac{6x}{6}+\frac{6}{6}=\frac{x^{2}}{3}-x+1$
