What is the answer to 1/x+x/(x-1)=1 ?

The answer to 1/x+x/(x-1)=1 is x= 1/2

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1/x+x/(x-1)=1

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

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

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

Multiply by LCM

x - 1 + x^{2} = x^{2} - x

Move

1

to the right side

x + x^{2} = x^{2} - x + 1

Subtract

x^{2} - x

from both sides

x + x^{2} - (x^{2} - x) = x^{2} - x + 1 - (x^{2} - x)

Simplify

2 x = 1

Divide both sides by

2

x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = \frac{1}{2}

\frac{c - 5}{5 - c} = 1

\frac{69}{( x - 74 )} = 3

\frac{5}{y - 2} + \frac{3}{y + 4} = 2

\frac{- 4}{13} = \frac{5}{x}

\frac{x}{x + 3} = 19