What is the answer to 1/(x-1)+2/x =0 ?

The answer to 1/(x-1)+2/x =0 is x= 2/3

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1/(x-1)+2/x =0

\frac{1}{x - 1} + \frac{2}{x} = 0

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

\frac{1}{x - 1} + \frac{2}{x} = 0

Multiply by LCM

x + 2 (x - 1) = 0

Expand

2 (x - 1) : 2 x - 2

x + 2 x - 2 = 0

Add similar elements:

x + 2 x = 3 x

3 x - 2 = 0

Move

2

to the right side

3 x = 2

Divide both sides by

3

x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = \frac{2}{3}

\frac{4}{3 + z} = \frac{6}{5}

x^{2} + \frac{5}{x} = 8

5 x^{- 3} = 135

9 - \frac{6 x}{x + 4} = - \frac{3}{x + 4}

6 - \frac{3 x}{x - 9} = - \frac{6}{x - 9}