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
To simplify the expression, we will factorize each polynomial, convert the division into multiplication, and then cancel out common factors. Step 1: Factorize all quadratic expressions. Factorize the first numerator, x^2-1: x^2-1 = (x-1)(x+1) Factorize the first denominator, x^2+x-2: x^2+x-2 = (x+2)(x-1) Factorize the second numerator, x^2-4x+3: x^2-4x+3 = (x-3)(x-1) Factorize the second denominator, x^2+4x+4: x^2+4x+4 = (x+2)^2 = (x+2)(x+2) Step 2: Substitute the factored expressions back into the original problem. ((x-1)(x+1))/((x+2)(x-1)) ÷ ((x-3)(x-1))/((x+2)(x+2)) Step 3: Convert the division into multiplication by inverting the second fraction. ((x-1)(x+1))/((x+2)(x-1)) × ((x+2)(x+2))/((x-3)(x-1)) Step 4: Cancel out common factors from the numerator and the denominator. Cancel one (x-1) from the numerator and one (x-1) from the denominator. Cancel one (x+2) from the numerator and one (x+2) from the denominator. = (x-1)(x+1)(x+2)(x-1) × (x+2)(x+2)(x-3)(x-1) = ((x+1))/(1) × ((x+2))/((x-3)(x-1)) Step 5: Multiply the remaining terms to get the simplified expression. = ((x+1)(x+2))/((x-3)(x-1)) The simplified expression is: ((x+1)(x+2))/((x-3)(x-1)) That's 2 down. 3 left today — send the next one.