Question

For which value of x does each expression make sense: square root of (x-2) / square root of (x-3)

Answer 1

• The expression makes sense when x > 3.

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Given expression:

• 
  `\cfrac{√(x-2) }{√(x-3) }`

The restrictions are:

• x - 2 ≥ 0, expression under square root can't be negative.
• x - 3 ≥ 0, same as above,
• x - 3 ≠ 0, denominator can't be zero.

Solve each and combine:

• x ≥ 2,
• x ≥ 3,
• x ≠ 3.

The common interval is x > 3.