What is the answer to 3-3/(3-1/x)=1 ?

The answer to 3-3/(3-1/x)=1 is x= 2/3

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3-3/(3-1/x)=1

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

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

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

Move

3

to the right side

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

Simplify

- \frac{3}{3 - \frac{1}{x}} : - \frac{3 x}{3 x - 1}

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

Multiply both sides by

3 x - 1

- 3 x = - 2 (3 x - 1)

Expand

- 2 (3 x - 1) : - 6 x + 2

- 3 x = - 6 x + 2

Move

6 x

to the left side

3 x = 2

Divide both sides by

3

x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{3}, x = 0

Combine undefined points with solutions:

x = \frac{2}{3}

x^{- 2} = 16

\frac{1}{x} = \frac{1}{4}

\frac{1}{x - 1} = 2

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

\frac{12}{x} = \frac{2}{18}