What is the answer to 1/(1+1/x)=16 ?

The answer to 1/(1+1/x)=16 is x=-16/15

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1/(1+1/x)=16

\frac{1}{1 + \frac{1}{x}} = 16

x = - \frac{16}{15}

Decimal Notation

x = - 1.06666 \dots

Solution steps

\frac{1}{1 + \frac{1}{x}} = 16

Simplify

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

\frac{x}{x + 1} = 16

Multiply both sides by

x + 1

x = 16 (x + 1)

Expand

16 (x + 1) : 16 x + 16

x = 16 x + 16

Move

16 x

to the left side

- 15 x = 16

Divide both sides by

- 15

x = - \frac{16}{15}

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = - \frac{16}{15}

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

\frac{4}{x - 2} - \frac{15}{x} = 2

y, \frac{- 2 x - y}{x + 2 y} = 0

\frac{18}{x ^{2} - 3 x} + 2 = \frac{6}{x - 3}

\frac{7}{x} - \frac{3}{4 x} = 5