Find the Domain ( square root of x+6)/(6+x)

Problem

√(,x+6)/(6+x)

Solution

1. Identify the constraints for the square root function. For the expression √(,x+6) to be defined in the real numbers, the radicand must be non-negative.

x+6≥0

2. Solve the inequality for x by subtracting 6 from both sides.

x≥−6

3. Identify the constraints for the rational function. The denominator of a fraction cannot be zero.

6+x≠0

4. Solve for the excluded value of x

x≠−6

5. Combine the two conditions. Since x must be greater than or equal to −6 but cannot be equal to −6 the domain is restricted to values strictly greater than −6

x>−6

6. Express the domain in interval notation.

(−6,∞)

Final Answer

Domain:(−6,∞)

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