Solve for y 0=(y(12-y))/((y^2-2y+12)^2)

Problem

0=(y*(12−y))/((y2−2*y+12)2)

Solution

1. Identify the condition for a fraction to equal zero. A fraction equals zero if and only if its numerator is zero and its denominator is non-zero.

2. Set the numerator equal to zero.

y*(12−y)=0

3. Apply the zero product property. This implies that either the first factor or the second factor must be zero.

y=0

12−y=0⇒y=12

4. Check the denominator for these values to ensure they do not result in division by zero. The denominator is (y2−2*y+12)2

5. Evaluate the denominator at y=0

(0−2*(0)+12)2=12=144

6. Evaluate the denominator at y=12

(12−2*(12)+12)2=(144−24+12)2=132=17424

7. Conclude that since the denominator is non-zero for both values, both are valid solutions.

Final Answer

y=0,12

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