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: Simplify the complex fraction inside the parenthesis. The complex fraction is (y^3)/(x^4)(y^4-y^3)/(x^4). To simplify, multiply the numerator by the reciprocal of the denominator: (y^3)/(x^4) · (x^4)/(y^4-y^3) Cancel out the x^4 terms: = (y^3)/(y^4-y^3) Factor out y^3 from the denominator: = (y^3)/(y^3(y-1)) Cancel out y^3 (assuming y ≠ 0): = (1)/(y-1) Step 2: Substitute the simplified complex fraction back into the original expression. The expression becomes: 2 - (1)/(y-1) Step 3: Combine the terms into a single fraction. To do this, find a common denominator, which is (y-1): = (2(y-1))/(y-1) - (1)/(y-1) Combine the numerators: = (2(y-1) - 1)/(y-1) Distribute the 2 in the numerator and simplify: = (2y - 2 - 1)/(y-1) = (2y - 3)/(y-1) The simplified expression is (2y-3)/(y-1).