Answer:
(1, 3) ∪ (5, ∞)
Explanation:
You want the solution to the inequality ((x -1)(x -5))/(x -3) > 0.
Sign changes
The sign of the function changes at values of x that make the factors zero, at x = 1, 3, 5. The function is positive for x > 5, so will also be positive for 1 < x < 3
The solution is ...
1 < x < 3 or 5 < x
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Additional comment
If any linear factor has an even degree (even multiplicity), there will not be a sign change. The numerator factors correspond to function zeros. The denominator factors correspond to function vertical asymptotes.
The attached graph shows zeros at x=1 and x=5, and a vertical asymptote with a sign change at x=3.