What is the limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6) ?

The limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6) is 5

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limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6)

x \to 3 lim (\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6})

5

Solution steps

x \to 3 lim (\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6})

Simplify

\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6} : \frac{x + 2}{x - 2}

= x \to 3 lim (\frac{x + 2}{x - 2})

Plug in the value

x = 3

= \frac{3 + 2}{3 - 2}

Simplify

= 5

What is the limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6) ?
The limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6) is 5