Answer
$\frac{-7}{6}$
Work Step by Step
According to the rules of simplification, we first need to simplify the expressions in the parenthesis and then move on to addition/subtraction. Therefore, we first multiply the fractions in parenthesis together and reduce these fractions by cancelling out the common factors in the numerators and denominators.
Step 1: $(\frac{2}{3})(-\frac{3}{4})-(\frac{5}{6})(\frac{4}{5})$
Step 2: $(\frac{2\times-3}{3\times4})-(\frac{5\times4}{6\times5})$
Step 3: $(\frac{2\times-1}{1\times4})-(\frac{1\times4}{6\times1})$
Step 4: $(\frac{1\times-1}{1\times2})-(\frac{1\times2}{3\times1})$
Then, we simplify the two fractions by finding the LCM of their denominators:
Step 5: $(\frac{-1}{2})-(\frac{2}{3})$
Step 6: $\frac{-1(3)-2(2)}{6}$
Step 7: $\frac{-3-4}{6}$
Step 8: $\frac{-7}{6}$
