What is the answer to (1+x)/x =sqrt(5) ?

The answer to (1+x)/x =sqrt(5) is x=(sqrt(5)+1)/4

Solve for x: (1+x)/x =sqrt(5)

The solution is x=(sqrt(5)+1)/4

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\frac{1 + x}{x} = 5

x = \frac{5 + 1}{4}

Decimal Notation

x = 0.80901 \dots

Solution steps

\frac{1 + x}{x} = 5

Multiply both sides by

x

1 + x = 5 x

Move

1

to the right side

x = 5 x - 1

Move

5 x

to the left side

x - 5 x = - 1

Factor

x - 5 x : (1 - 5) x

(1 - 5) x = - 1

Divide both sides by

1 - 5

x = \frac{5 + 1}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{5 + 1}{4}

\frac{24}{2 x} = 1 + x

\frac{5 - x}{x + 1} = \frac{6}{2}

(x + 4)^{- 1} = x^{- 1} + x

\frac{1}{10} = \frac{18.5}{x}

\frac{1}{2 x} = - 18

What is the answer to (1+x)/x =sqrt(5) ?
The answer to (1+x)/x =sqrt(5) is x=(sqrt(5)+1)/4
Solve for x: (1+x)/x =sqrt(5)
The solution is x=(sqrt(5)+1)/4