Evaluate the Limit

Problem

(lim_x→5)((x2−6*x+5)/(x−5))

Solution

1. Identify the indeterminate form by substituting x=5 into the expression, which results in 0/0

2. Factor the numerator x2−6*x+5 by finding two numbers that multiply to 5 and add to −6

3. Rewrite the quadratic expression as (x−5)*(x−1)

4. Cancel the common factor (x−5) from the numerator and the denominator, noting that x≠5 when evaluating the limit.

5. Substitute x=5 into the remaining simplified expression x−1

Final Answer

(lim_x→5)((x2−6*x+5)/(x−5))=4

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