Evaluate the Limit

Problem

(lim_x→2)((x2−5*x+6)/(x−2))

Solution

1. Identify the indeterminate form by substituting x=2 into the expression, which results in 0/0

2. Factor the quadratic expression in the numerator by finding two numbers that multiply to 6 and add to −5

x2−5*x+6=(x−2)*(x−3)

3. Simplify the expression by canceling the common factor (x−2) from the numerator and the denominator.

((x−2)*(x−3))/(x−2)=x−3

4. Evaluate the limit by substituting x=2 into the remaining linear expression.

2−3=−1

Final Answer

(lim_x→2)((x2−5*x+6)/(x−2))=−1

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