What is the answer to x/(1-x)=10 ?

The answer to x/(1-x)=10 is x= 10/11

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x/(1-x)=10

\frac{x}{1 - x} = 10

x = \frac{10}{11}

Decimal Notation

x = 0.90909 \dots

Solution steps

\frac{x}{1 - x} = 10

Multiply both sides by

1 - x

x = 10 (1 - x)

Expand

10 (1 - x) : 10 - 10 x

x = 10 - 10 x

Move

10 x

to the left side

11 x = 10

Divide both sides by

11

x = \frac{10}{11}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{10}{11}

- \frac{4}{x + 1} - \frac{3}{x} = - 2

\frac{1}{2 x} + \frac{5}{3} = 3

- \frac{8}{y} = 6

\frac{- 24}{x + 5} = \frac{- 9}{x}

\frac{x - 5}{3 x} + 1 = \frac{x + 4}{x}