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

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

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

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

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

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

Simplify

\frac{1}{1 + \frac{1}{x}} : \frac{x}{x + 1}

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

Multiply both sides by

x + 1

2 x + 1 = 0

Move

1

to the right side

2 x = - 1

Divide both sides by

2

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = - \frac{1}{2}

\frac{100}{x} = \frac{30}{26}

\frac{4}{5 x} = - 20

\frac{100}{x} = \frac{30}{27}

\frac{100}{x} = \frac{30}{28}

1 - \frac{25}{x ^{2}} = 0