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
You're on a roll — Step 1: Identify the given algebraic expression. The expression is: (x^2)/((x-2)^2) Step 2: Expand the denominator. The denominator is a binomial squared, (x-2)^2. Using the formula (a-b)^2 = a^2 - 2ab + b^2: (x-2)^2 = x^2 - 2(x)(2) + 2^2 (x-2)^2 = x^2 - 4x + 4 Step 3: Rewrite the expression with the expanded denominator. Substitute the expanded denominator back into the expression: (x^2)/(x^2 - 4x + 4) Step 4: Determine the domain of the expression. For the expression to be defined, the denominator cannot be zero. (x-2)^2 ≠ 0 x-2 ≠ 0 x ≠ 2 The expression is defined for all real numbers x except x=2. The simplified form of the expression is: (x^2)/(x^2 - 4x + 4) What's next?