What is the answer to 1/(1+\frac{1){1+x}}=5 ?

The answer to 1/(1+\frac{1){1+x}}=5 is x=-9/4

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1/(1+\frac{1){1+x}}=5

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

x = - \frac{9}{4}

Decimal Notation

x = - 2.25

Solution steps

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

Simplify

\frac{1}{1 + \frac{1}{1 + x}} : \frac{1 + x}{x + 2}

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

Multiply both sides by

x + 2

1 + x = 5 (x + 2)

Expand

5 (x + 2) : 5 x + 10

1 + x = 5 x + 10

Move

1

to the right side

x = 5 x + 9

Move

5 x

to the left side

- 4 x = 9

Divide both sides by

- 4

x = - \frac{9}{4}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = - 1

Combine undefined points with solutions:

x = - \frac{9}{4}

0.0127 = \frac{x ^{2}}{( 0.267 - x )}

\frac{6}{x + 7} = \frac{4}{x + 7} + 2

0.325 = \frac{39}{b}

\frac{- g + f}{a} = h^{3}

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

What is the answer to 1/(1+\frac{1){1+x}}=5 ?
The answer to 1/(1+\frac{1){1+x}}=5 is x=-9/4
Solve for x: 1/(1+\frac{1){1+x}}=5
The solution is x=-9/4