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
Here are the simplified expressions: i) Simplify (7m)/(8) - (7m)/(12) Step 1: Find the least common multiple (LCM) of the denominators 8 and 12. The multiples of 8 are 8, 16, 24, 32, ... The multiples of 12 are 12, 24, 36, ... The LCM of 8 and 12 is 24. Step 2: Rewrite each fraction with the common denominator. (7m)/(8) = (7m × 3)/(8 × 3) = (21m)/(24) (7m)/(12) = (7m × 2)/(12 × 2) = (14m)/(24) Step 3: Subtract the fractions. (21m)/(24) - (14m)/(24) = (21m - 14m)/(24) = (7m)/(24) The simplified expression is (7m)/(24). ii) Simplify (4x+2)/(12) - (3x+2)/(8) Step 1: Find the least common multiple (LCM) of the denominators 12 and 8. The LCM of 12 and 8 is 24. Step 2: Rewrite each fraction with the common denominator. (4x+2)/(12) = ((4x+2) × 2)/(12 × 2) = (8x+4)/(24) (3x+2)/(8) = ((3x+2) × 3)/(8 × 3) = (9x+6)/(24) Step 3: Subtract the fractions. Remember to distribute the negative sign to all terms in the second numerator. (8x+4)/(24) - (9x+6)/(24) = ((8x+4) - (9x+6))/(24) = (8x+4 - 9x - 6)/(24) Step 4: Combine like terms in the numerator. = ((8x - 9x) + (4 - 6))/(24) = (-x - 2)/(24) This can also be written as: = -(x+2)/(24) The simplified expression is -(x+2)/(24). That's 2 down. 3 left today — send the next one.