What is the limit as x approaches 2 of (8/x-4)/(2-x) ?

The limit as x approaches 2 of (8/x-4)/(2-x) is 2

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limit as x approaches 2 of (8/x-4)/(2-x)

x \to 2 lim (\frac{\frac{8}{x} - 4}{2 - x})

2

Solution steps

x \to 2 lim (\frac{\frac{8}{x} - 4}{2 - x})

Simplify

\frac{\frac{8}{x} - 4}{2 - x} : \frac{4}{x}

= x \to 2 lim (\frac{4}{x})

Plug in the value

x = 2

= \frac{4}{2}

Simplify

= 2

What is the limit as x approaches 2 of (8/x-4)/(2-x) ?
The limit as x approaches 2 of (8/x-4)/(2-x) is 2