Solve 1/1+frac{1{x}}=0.203

$$\frac { 1 } { 1 + \frac { 1 } { x } } = 0.203$$

Solve for x

$$x=\frac{203}{797}\approx 0.254705144$$

Steps for Solving Linear Equation

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

$$\frac{1}{\frac{x}{x}+\frac{1}{x}}=0.203$$

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

$$\frac{1}{\frac{x+1}{x}}=0.203$$

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}.

$$\frac{x}{x+1}=0.203$$

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

$$x=0.203\left(x+1\right)$$

Use the distributive property to multiply 0.203 by x+1.

$$x=0.203x+0.203$$

Subtract 0.203x from both sides.

$$x-0.203x=0.203$$

Combine x and -0.203x to get 0.797x.

$$0.797x=0.203$$

Divide both sides by 0.797.

$$x=\frac{0.203}{0.797}$$

Expand \frac{0.203}{0.797} by multiplying both numerator and the denominator by 1000.

$$x=\frac{203}{797}$$