Find the Domain 14/(3x-12)-(2+x)/(x-4)=3/(8-2x)-3

Problem

14/(3*x−12)−(2+x)/(x−4)=3/(8−2*x)−3

Solution

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

2. Factor each denominator to find the values of x that would result in division by zero.

3. Analyze the first denominator: 3*x−12=3*(x−4) Setting this to zero gives x=4

4. Analyze the second denominator: x−4 Setting this to zero gives x=4

5. Analyze the third denominator: 8 - 2x = 2(4 - x).S*e*t*t*i*n*g*t*h*i*s(t)*o*z*e*r*o*g*i*v*e*s() = 4$.

6. Exclude the value x=4 from the set of all real numbers, as it makes all denominators zero.

7. State the domain in interval notation or set-builder notation.

Final Answer

Domain={[x∈ℝ,x≠4]}

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