Find the Domain 1/(x-1)-2/(2x-1)=1

Problem

1/(x−1)−2/(2*x−1)=1

Solution

1. Identify the denominators in the equation that contain the variable x

2. Set each denominator equal to zero to find the values that would make the expression undefined, as division by zero is not allowed.

3. Solve the first equation x−1=0 to find the first excluded value.

x−1=0

x=1

4. Solve the second equation 2*x−1=0 to find the second excluded value.

2*x−1=0

2*x=1

x=1/2

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

Final Answer

Domain:{[x∈ℝ,x≠1,x≠1/2]}

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