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: Identify when the expression is undefined. A rational expression is undefined when its denominator is equal to zero. The given expression is (y^2 - 9y + 18)/(y^2 + 4y - 21). The denominator is y^2 + 4y - 21. Step 2: Set the denominator to zero and solve for y. y^2 + 4y - 21 = 0 We need to factor the quadratic equation. We look for two numbers that multiply to -21 and add to 4. These numbers are 7 and -3. (y + 7)(y - 3) = 0 Step 3: Find the values of y. Set each factor equal to zero: y + 7 = 0 y = -7 y - 3 = 0 y = 3 The values of y for which the expression is undefined are y = -7 and y = 3. The values of y for which the expression is undefined are y = -7, 3.