This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Write down the given equation and simplify the signs. The equation is: (3)/(4) + ((-4))/(3) + (5)/(6) = ((-4))/(3) + (5)/(6) + (3)/(4) Simplify the signs: (3)/(4) - (4)/(3) + (5)/(6) = -(4)/(3) + (5)/(6) + (3)/(4) Step 2: Evaluate the Left Hand Side (LHS). To add and subtract fractions, find a common denominator. The denominators are 4, 3, and 6. The least common multiple (LCM) of 4, 3, and 6 is 12. Convert each fraction to have a denominator of 12: (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) -(4)/(3) = -(4 × 4)/(3 × 4) = -(16)/(12) (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) Now, add these fractions: LHS = (9)/(12) - (16)/(12) + (10)/(12) = (9 - 16 + 10)/(12) LHS = (-7 + 10)/(12) = (3)/(12) Simplify the fraction: LHS = (1)/(4) Step 3: Evaluate the Right Hand Side (RHS). Using the same common denominator (12) for the fractions on the RHS: -(4)/(3) = -(16)/(12) (5)/(6) = (10)/(12) (3)/(4) = (9)/(12) Now, add these fractions: RHS = -(16)/(12) + (10)/(12) + (9)/(12) = (-16 + 10 + 9)/(12) RHS = (-6 + 9)/(12) = (3)/(12) Simplify the fraction: RHS = (1)/(4) Step 4: Compare LHS and RHS. Since LHS = (1)/(4) and RHS = (1)/(4), both sides are equal. Therefore, the given equation is true. (1)/(4) = (1)/(4) That's 2 down. 3 left today — send the next one.