we have been given an expression [tex]\frac{\frac{2}{3}}{-4}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]. We are asked to simplify our given expression.
Using quotient rule [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:
[tex]\frac{2}{3\cdot -4}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]
[tex]\frac{2}{-12}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]
Now, we will combine like terms:
[tex]\frac{2}{-12}-\left(\frac{1-8}{6}\right)[/tex]
[tex]\frac{2}{-12}-\left(\frac{-7}{6}\right)[/tex]
[tex]-\frac{2}{12}+\frac{7}{6}[/tex]
[tex]-\frac{1}{6}+\frac{7}{6}[/tex]
Let us combine like terms:
[tex]\frac{-1+7}{6}[/tex]
[tex]\frac{6}{6}=1[/tex]
Therefore, our expression simplifies to 1.
