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: Rewrite the division as multiplication by inverting the second fraction. To divide by a fraction, multiply by its reciprocal. (21x^2)/(8xy) ÷ (7xy)/(12x^2) = (21x^2)/(8xy) × (12x^2)/(7xy) Step 2: Multiply the numerators and the denominators. (21x^2 × 12x^2)/(8xy × 7xy) Step 3: Combine the terms in the numerator and denominator. Multiply the coefficients and add the exponents for like variables. Numerator: 21 × 12 × x^2 × x^2 = 252x^2+2 = 252x^4 Denominator: 8 × 7 × x × x × y × y = 56x^1+1y^1+1 = 56x^2y^2 So the expression becomes: (252x^4)/(56x^2y^2) Step 4: Simplify the fraction by dividing the coefficients and subtracting the exponents for like variables. Divide the numerical coefficients: (252)/(56). Both are divisible by 7: 252 ÷ 7 = 36, 56 ÷ 7 = 8. So (36)/(8). Both are divisible by 4: 36 ÷ 4 = 9, 8 ÷ 4 = 2. So (9)/(2). Simplify the x terms: (x^4)/(x^2) = x^4-2 = x^2. The y terms are only in the denominator: (1)/(y^2). Combining these simplified parts: (9x^2)/(2y^2) The simplified expression is: (9x^2)/(2y^2) That's 2 down. 3 left today — send the next one.