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 fractional part of the expression. The given expression is 2 - (y^1)/(3)y^(1)/(4) - y^(1)/(3). Let's focus on the fraction (y^1)/(3)y^(1)/(4) - y^(1)/(3). To simplify the exponents, find the least common multiple of the denominators of the fractions (1)/(3) and (1)/(4), which is 12. Let u = y^(1)/(12). Then y^(1)/(3) = y^(4)/(12) = (y^(1)/(12))^4 = u^4. And y^(1)/(4) = y^(3)/(12) = (y^(1)/(12))^3 = u^3. Substitute these into the fraction: (u^4)/(u^3 - u^4) Step 2: Factor the denominator and simplify the fraction. Factor out u^3 from the denominator: (u^4)/(u^3(1 - u)) Cancel u^3 from the numerator and denominator: (u)/(1 - u) Step 3: Substitute the simplified fraction back into the original expression. The expression now becomes: 2 - (u)/(1 - u) Step 4: Combine the terms by finding a common denominator. The common denominator is 1 - u. (2(1 - u))/(1 - u) - (u)/(1 - u) (2 - 2u - u)/(1 - u) (2 - 3u)/(1 - u) Step 5: Substitute back u = y^(1)/(12). (2 - 3y^1)/(12)1 - y^(1)/(12) The final answer is (2 - 3y^1)/(12)1 - y^(1)/(12).