Solve 1.4025=1+1/1+frac{1{x}}

$$1.4025 = 1 + \frac { 1 } { 1 + \frac { 1 } { x } }$$

Solve for x

$$x=\frac{161}{239}\approx 0.673640167$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$1.4025=1+\frac{1}{\frac{x}{x}+\frac{1}{x}}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$1.4025=1+\frac{1}{\frac{x+1}{x}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 1 by \frac{x+1}{x} by multiplying 1 by the reciprocal of \frac{x+1}{x}.

$$1.4025=1+\frac{x}{x+1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+1}{x+1}.

$$1.4025=\frac{x+1}{x+1}+\frac{x}{x+1}$$

Since \frac{x+1}{x+1} and \frac{x}{x+1} have the same denominator, add them by adding their numerators.

$$1.4025=\frac{x+1+x}{x+1}$$

Combine like terms in x+1+x.

$$1.4025=\frac{2x+1}{x+1}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2x+1}{x+1}=1.4025$$

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$2x+1=1.4025\left(x+1\right)$$

Use the distributive property to multiply 1.4025 by x+1.

$$2x+1=1.4025x+1.4025$$

Subtract 1.4025x from both sides.

$$2x+1-1.4025x=1.4025$$

Combine 2x and -1.4025x to get 0.5975x.

$$0.5975x+1=1.4025$$

Subtract 1 from both sides.

$$0.5975x=1.4025-1$$

Subtract 1 from 1.4025 to get 0.4025.

$$0.5975x=0.4025$$

Divide both sides by 0.5975.

$$x=\frac{0.4025}{0.5975}$$

Expand \frac{0.4025}{0.5975} by multiplying both numerator and the denominator by 10000.

$$x=\frac{4025}{5975}$$

Reduce the fraction \frac{4025}{5975} to lowest terms by extracting and canceling out 25.

$$x=\frac{161}{239}$$