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

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

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

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

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

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

Multiply by LCM

x (x + 1) + x + 1 = x^{2}

Expand

x (x + 1) : x^{2} + x

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

Add similar elements:

x + x = 2 x

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

Move

1

to the right side

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

Move

x^{2}

to the left side

2 x = - 1

Divide both sides by

2

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

x = - \frac{1}{2}

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

x^{- 2} + 6 x^{- 1} - 16 = 0

r, F g = \frac{g m d}{r}

\frac{x}{4} = \frac{8}{2 x}

\frac{8}{3} = \frac{7}{k - 2}