How do you evaluate the limit -(x^2-3x)/(x-3) as x approaches 3?

1 Answer
Steve M
Dec 18, 2016

lim_(x rarr 3) -(x^2-3x)/(x-3) = -3

Explanation:

lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) -(x(x-3))/(x-3)
lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) (-x)
lim_(x rarr 3) -(x^2-3x)/(x-3) = -3

Which we can confirm graphically;
graph{-(x^2-3x)/(x-3) [-10, 10, -5, 5]}

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