What is (1+1/x)/(2-1/x) ?

The solution to (1+1/x)/(2-1/x) is (x+1)/(2x-1)

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simplify (1+1/x)/(2-1/x)

simplify

\frac{1 + \frac{1}{x}}{2 - \frac{1}{x}}

\frac{x + 1}{2 x - 1}

Solution steps

\frac{1 + \frac{1}{x}}{2 - \frac{1}{x}}

Join

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

= \frac{\frac{x + 1}{x}}{2 - \frac{1}{x}}

Join

2 - \frac{1}{x} : \frac{2 x - 1}{x}

= \frac{\frac{x + 1}{x}}{\frac{2 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 ( 2 x - 1 )}

Cancel the common factor:

x

= \frac{x + 1}{2 x - 1}

sin (θ) cot (θ)

(1 - cos^{2} (x)) (1 + cot^{2} (x))

(3 x - 7) (2 x + 1)

- 12 + 9 - 2 \cdot (- 3^{2})

\frac{\frac{5}{7}}{\frac{3}{7}} + \frac{1}{2} \cdot \frac{8}{3} - \frac{\frac{2}{5}}{\frac{4}{5}}