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

Problem

x/√(,x−6)

Solution

1. Identify the constraints for the expression to be defined. For a fraction, the denominator cannot be zero. For a square root, the radicand must be non-negative.

2. Combine these constraints. Since the square root is in the denominator, the expression inside the square root must be strictly greater than zero.

3. Set up the inequality for the radicand.

x−6>0

4. Solve the inequality for x by adding 6 to both sides.

x>6

5. Express the domain in interval notation. Since x must be strictly greater than 6 the interval starts at 6 with a parenthesis and goes to infinity.

(6,∞)

Final Answer

Domain: *(6,∞)

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