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

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

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

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

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

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

Multiply by LCM

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

Move

1

to the right side

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

Subtract

x^{2} - x

from both sides

x^{2} + x - (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 = 1, x = 0

Combine undefined points with solutions:

x = \frac{1}{2}

\frac{2}{3} - \frac{x - 6}{x - 5} = 0

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

x - \frac{1}{x} = \frac{8}{3}

\frac{8}{( x - 2 ) ^{3}} = 0

\frac{1}{x - 3} + 2 = \frac{9}{x - 3}