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

The solution to (x+1)/(2-1/(x-1)) is ((x+1)(x-1))/(2x-3)

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

simplify

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

\frac{( x + 1 ) ( x - 1 )}{2 x - 3}

Solution steps

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

Join

2 - \frac{1}{x - 1} : \frac{2 x - 3}{x - 1}

= \frac{x + 1}{\frac{2 x - 3}{x - 1}}

Apply the fraction rule:

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

= \frac{( x + 1 ) ( x - 1 )}{2 x - 3}

\frac{240}{60}

(x + 3) (2 x^{2} + 4 x - 4)

\frac{( x ^{2} - 2 x )}{( - 3 x ^{2} + 9 x - 6 )}

\frac{10}{50}

16 - 2 (4 + 3 x)

What is (x+1)/(2-1/(x-1)) ?
The solution to (x+1)/(2-1/(x-1)) is ((x+1)(x-1))/(2x-3)