What is the answer to 2x= 1/x+1 ?

The answer to 2x= 1/x+1 is x=1,x=-1/2

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2x= 1/x+1

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

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

Decimal Notation

x = 1, x = - 0.5

Solution steps

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

Multiply both sides by

x

2 x^{2} = 1 + x

Solve

2 x^{2} = 1 + x : x = 1, x = - \frac{1}{2}

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

7 - \frac{13}{x} = 4 + \frac{2}{x}

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

2 \frac{2}{9} = \frac{- 4}{5 m}

\frac{2}{x + 4} - 5 = \frac{27}{x + 4}

\frac{1}{2 x + 5} = \frac{x}{11 x + 8}