Find the Domain y/(y^2-2y)

Problem

y/(y2−2*y)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

Denominator≠0

2. Set the denominator expression equal to zero to find the excluded values of y

y2−2*y=0

3. Factor the quadratic expression by taking out the greatest common factor, which is y

y*(y−2)=0

4. Solve for y by setting each factor to zero using the zero product property.

y=0

y−2=0⇒y=2

5. Exclude these values from the set of all real numbers to define the domain.

y≠0

y≠2

Final Answer

Domain: *{y|y∈ℝ,y≠0,y≠2}

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