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

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

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

simplify

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

x

Solution steps

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

Apply rule:

(a) = a

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

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

Join

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

= \frac{1}{\frac{1}{x}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x}{1}

Apply the fraction rule:

\frac{a}{1} = a

= x

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

\frac{\frac{4}{9} + \frac{5}{6}}{\frac{3}{5}}

\frac{x + 3}{x - 8} - \frac{x - 4}{x}

\frac{11 - 3}{11 + 3}