What is (1+1/x)/(1/x-3) ?

The solution to (1+1/x)/(1/x-3) is (x+1)/(-3x+1)

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simplify (1+1/x)/(1/x-3)

simplify

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

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

Solution steps

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

Join

1 + \frac{1}{x} : \frac{x + 1}{x}

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

Join

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

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

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

Cancel the common factor:

x

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

10 - 1

3 + - 16

2 (a + b)^{3}

\frac{6 + - 24}{4}

- 3.005 - 4.7 + (- 2)