What is the limit as x approaches 3-of (x+3)/(x-3) ?

The limit as x approaches 3-of (x+3)/(x-3) is -infinity

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limit as x approaches 3-of (x+3)/(x-3)

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

- \infty

Solution steps

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

\frac{x + 3}{x - 3} = (x + 3) \frac{1}{x - 3}

= x \to 3 - lim ((x + 3) \frac{1}{x - 3})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 3 - lim (x + 3) \cdot x \to 3 - lim (\frac{1}{x - 3})

x \to 3 - lim (x + 3) = 6

x \to 3 - lim (\frac{1}{x - 3}) = - \infty

= 6 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 2 lim (x^{5} - 2 x^{4} + x - 7)

x \to - 1 + lim (x^{2} - 1)

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

x \to - 2 lim (3 x^{2} + 2 x - 1)

x \to 2 lim (5 x + 6)

What is the limit as x approaches 3-of (x+3)/(x-3) ?
The limit as x approaches 3-of (x+3)/(x-3) is -infinity