Evaluate the Limit

Problem

(lim_x→−1)((6*x+5)/(5*x−6))

Solution

1. Identify the type of limit by checking if the denominator is zero at the target value x=−1

2. Evaluate the denominator at x=−1

5*(−1)−6=−11

3. Apply the direct substitution property since the function is a rational function and the denominator is not zero at x=−1

(6*(−1)+5)/(5*(−1)−6)

4. Simplify the numerator and the denominator to find the final value.

(−6+5)/(−5−6)=(−1)/(−11)

5. Reduce the fraction by canceling the negative signs.

1/11

Final Answer

(lim_x→−1)((6*x+5)/(5*x−6))=1/11

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