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. The equation is: -(5)/(7) + (7)/(5) + (-(3)/(2)) = (7)/(5) + (-(3)/(2)) + (-(5)/(7)) Simplify the signs: -(5)/(7) + (7)/(5) - (3)/(2) = (7)/(5) - (3)/(2) - (5)/(7) Step 2: Evaluate the Left Hand Side (LHS). To add and subtract fractions, find a common denominator. The denominators are 7, 5, and 2. The least common multiple (LCM) of 7, 5, and 2 is 7 × 5 × 2 = 70. Convert each fraction to have a denominator of 70: -(5)/(7) = -(5 × 10)/(7 × 10) = -(50)/(70) (7)/(5) = (7 × 14)/(5 × 14) = (98)/(70) -(3)/(2) = -(3 × 35)/(2 × 35) = -(105)/(70) Now, add these fractions: -(50)/(70) + (98)/(70) - (105)/(70) = (-50 + 98 - 105)/(70) (48 - 105)/(70) = (-57)/(70) So, LHS = -(57)/(70). Step 3: Evaluate the Right Hand Side (RHS). Using the same common denominator (70) for the fractions on the RHS: (7)/(5) = (98)/(70) -(3)/(2) = -(105)/(70) -(5)/(7) = -(50)/(70) Now, add these fractions: (98)/(70) - (105)/(70) - (50)/(70) = (98 - 105 - 50)/(70) (-7 - 50)/(70) = (-57)/(70) So, RHS = -(57)/(70). Step 4: Compare LHS and RHS. Since LHS = -(57)/(70) and RHS = -(57)/(70), both sides are equal. Therefore, the given equation is true. The equation is true. -(57)/(70) = -(57)/(70) Send me the next one 📸