Find the Domain 3/x+6/(x-2)=12/(x^2-2x)

Problem

3/x+6/(x−2)=12/(x2−2*x)

Solution

1. Identify the denominators in the equation to determine where the expression is undefined.

2. Factor the quadratic denominator in the term on the right side of the equation.

x2−2*x=x*(x−2)

3. Set each unique factor in the denominators to zero, as division by zero is undefined.

x=0

x−2=0

4. Solve for the excluded values of x

x=0

x=2

5. State the domain as all real numbers except for the values that make any denominator zero.

{[x∈ℝ,x≠0,x≠2]}

Final Answer

Domain:(−∞,0)∪(0,2)∪(2,∞)

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