What is 1-x/(1+\frac{x){1/(x-1)}} ?

The solution to 1-x/(1+\frac{x){1/(x-1)}} is 1-x/(1+x(x-1))

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simplify 1-x/(1+\frac{x){1/(x-1)}}

simplify

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

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

Solution steps

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

Apply the fraction rule:

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

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

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

Apply the fraction rule:

\frac{a}{1} = a

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

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

\frac{4}{5 + 1}

3 (x + 6) + 4 (2 x - 5)

\frac{72}{36}

2 7^{9^{- 4^{- 2^{- 1}}}}

\frac{x ^{2} - 10 x + 25}{x ^{2} - 25}

What is 1-x/(1+\frac{x){1/(x-1)}} ?
The solution to 1-x/(1+\frac{x){1/(x-1)}} is 1-x/(1+x(x-1))