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

You're on a roll — Step 1: Write down the given expression. -((3)/(11) × ((-5))/(6)) - ((9)/(12) ÷ (3)/(4)) - ((5)/(13) × ((-6))/(15)) Step 2: Evaluate the first term: -((3)/(11) × ((-5))/(6)). First, multiply the fractions inside the parenthesis: (3)/(11) × (-5)/(6) = (3 × (-5))/(11 × 6) = (-15)/(66) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 3: (-15 ÷ 3)/(66 ÷ 3) = (-5)/(22) Now apply the negative sign outside the parenthesis: -((-5)/(22)) = (5)/(22) Step 3: Evaluate the second term: -((9)/(12) ÷ (3)/(4)). First, perform the division inside the parenthesis. To divide by a fraction, multiply by its reciprocal: (9)/(12) ÷ (3)/(4) = (9)/(12) × (4)/(3) Multiply the numerators and denominators: (9 × 4)/(12 × 3) = (36)/(36) = 1 Now apply the negative sign outside the parenthesis: -(1) = -1 Step 4: Evaluate the third term: -((5)/(13) × ((-6))/(15)). First, multiply the fractions inside the parenthesis: (5)/(13) × (-6)/(15) = (5 × (-6))/(13 × 15) = (-30)/(195) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 15: (-30 ÷ 15)/(195 ÷ 15) = (-2)/(13) Now apply the negative sign outside the parenthesis: -((-2)/(13)) = (2)/(13) Step 5: Combine the results from Step 2, Step 3, and Step 4. The expression becomes: (5)/(22) - 1 + (2)/(13) To add and subtract these fractions, find a common denominator. The least common multiple (LCM) of 22 and 13 is 22 × 13 = 286. Convert each term to have a denominator of 286: (5)/(22) = (5 × 13)/(22 × 13) = (65)/(286) 1 = (286)/(286) (2)/(13) = (2 × 22)/(13 × 22) = (44)/(286) Now combine the fractions: (65)/(286) - (286)/(286) + (44)/(286) = (65 - 286 + 44)/(286) (109 - 286)/(286) = (-177)/(286) The final answer is -(177)/(286). Got more? Send 'em!