What is the answer to x=4+1/(1+1/x) ?

The answer to x=4+1/(1+1/x) is x=2(1+sqrt(2)),x=2(1-sqrt(2))

Solve for x: x=4+1/(1+1/x)

The solution is x=2(1+sqrt(2)),x=2(1-sqrt(2))

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x = 4 + \frac{1}{1 + \frac{1}{x}}

x = 2 (1 + 2), x = 2 (1 - 2)

Decimal Notation

x = 4.82842 \dots, x = - 0.82842 \dots

Solution steps

x = 4 + \frac{1}{1 + \frac{1}{x}}

Simplify

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

x = 4 + \frac{x}{x + 1}

Multiply both sides by

x + 1

x (x + 1) = 4 (x + 1) + x

Solve

x (x + 1) = 4 (x + 1) + x : x = 2 (1 + 2), x = 2 (1 - 2)

x = 2 (1 + 2), x = 2 (1 - 2)

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = 2 (1 + 2), x = 2 (1 - 2)

\frac{10}{x} = 7

\frac{3}{k} = 2

\frac{467}{x} = 15

k, c = \frac{k}{n ( 1 - k )}

\frac{12}{x - 1} - \frac{8}{x} = 2

What is the answer to x=4+1/(1+1/x) ?
The answer to x=4+1/(1+1/x) is x=2(1+sqrt(2)),x=2(1-sqrt(2))
Solve for x: x=4+1/(1+1/x)
The solution is x=2(1+sqrt(2)),x=2(1-sqrt(2))