Find the Domain (-14x)/(6x^2-x^2-2)

Problem

Domain of (−14*x)/(6*x2−x2−2)

Solution

1. Simplify the expression in the denominator by combining the like terms 6*x2 and −x2

6*x2−x2−2=5*x2−2

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

5*x2−2≠0

3. Solve the equation for x to find the excluded values by first isolating the x2 term.

5*x2=2

x2=2/5

4. Extract the square root of both sides to find the specific values of x that must be excluded from the domain.

x=±√(,2/5)

5. Rationalize the denominator of the excluded values to provide the answer in standard form.

x=±√(,10)/5

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

Final Answer

Domain: *{x|x∈ℝ,x≠±√(,10)/5}

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