For what values of y is the rational expression racy2 - 9y + 18y2 + 4y − 21 undefined?

Question

ScanSolve AI Tutor · Accepted 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 (y² − 9y + 18)/(y² + 4y − 21). The denominator is y² + 4y − 21. Step 2: Set the denominator to zero and solve for y. y² + 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.

For what values of y is the rational expression racy2 - 9y + 18y2 + 4y - 21 undefined?

Answer

Step-by-step solution

Identify when the expression is undefined.

Set the denominator to zero and solve for $y$ .

Find the values of $y$ .

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