Evaluate the expression: - (3/11 -5/6) - (9/12 / 3/4) - (5/13 -6/15)

$-\left(\frac{3}{11} \times \frac{(-5)}{6}\right)$.
First, multiply the fractions inside the parenthesis:

$$\frac{3}{11} \times \frac{-5}{6} = \frac{3 \times (-5)}{11 \times 6} = \frac{-15}{66}$$

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 3:

$$\frac{-15 \div 3}{66 \div 3} = \frac{-5}{22}$$

Now apply the negative sign outside the parenthesis:

$$-\left(\frac{-5}{22}\right) = \frac{5}{22}$$

$-\left(\frac{9}{12} \div \frac{3}{4}\right)$.
First, perform the division inside the parenthesis. To divide by a fraction, multiply by its reciprocal:

$$\frac{9}{12} \div \frac{3}{4} = \frac{9}{12} \times \frac{4}{3}$$

Multiply the numerators and denominators:

$$\frac{9 \times 4}{12 \times 3} = \frac{36}{36} = 1$$

Now apply the negative sign outside the parenthesis:

$$-(1) = -1$$

$-\left(\frac{5}{13} \times \frac{(-6)}{15}\right)$.
First, multiply the fractions inside the parenthesis:

$$\frac{5}{13} \times \frac{-6}{15} = \frac{5 \times (-6)}{13 \times 15} = \frac{-30}{195}$$

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 15:

$$\frac{-30 \div 15}{195 \div 15} = \frac{-2}{13}$$

Now apply the negative sign outside the parenthesis:

$$-\left(\frac{-2}{13}\right) = \frac{2}{13}$$

The expression becomes:

$$\frac{5}{22} - 1 + \frac{2}{13}$$

To add and subtract these fractions, find a common denominator. The least common multiple (LCM) of 22 and 13 is $22 \times 13 = 286$.
Convert each term to have a denominator of 286:

$$\frac{5}{22} = \frac{5 \times 13}{22 \times 13} = \frac{65}{286}$$ $$1 = \frac{286}{286}$$ $$\frac{2}{13} = \frac{2 \times 22}{13 \times 22} = \frac{44}{286}$$

Now combine the fractions:

$$\frac{65}{286} - \frac{286}{286} + \frac{44}{286} = \frac{65 - 286 + 44}{286}$$ $$\frac{109 - 286}{286} = \frac{-177}{286}$$

The final answer is $-\frac{177}{286}$.