Elementary Algebra

$-\frac{31}{36}$
First, we will find the LCM of the two denominators. Upon inspection, we find that 36 as it is the lowest number that is a multiple of 4,6, and 9. Therefore, $\frac{3}{4}-\frac{5}{6}-\frac{7}{9}=\frac{3(9)-5(6)-7(4)}{36}$ Now, we will simplify the expression: Step 1: $\frac{3(9)-5(6)-7(4)}{36}$ Step 2: $\frac{27-30-28}{36}$ Step 3: $\frac{-3-28}{36}$ Step 4: $\frac{-31}{36}$