What is the limit as x approaches 3 of (3/x-1)/(x-3) ?

The limit as x approaches 3 of (3/x-1)/(x-3) is -1/3

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limit as x approaches 3 of (3/x-1)/(x-3)

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

- \frac{1}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

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

Simplify

\frac{\frac{3}{x} - 1}{x - 3} : - \frac{1}{x}

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

Plug in the value

x = 3

= - \frac{1}{3}

\int_{1}^{\infty} \frac{2}{x ^{3}} d x

2 y^{^{''}} + 4 y = 0

\frac{d}{d x} (\frac{1}{x ( 1 + ln ( x ) )})

\int x (x + 3)^{2} d x

What is the limit as x approaches 3 of (3/x-1)/(x-3) ?
The limit as x approaches 3 of (3/x-1)/(x-3) is -1/3