Solve 1/1-1{1+frac{1/x}}=2Rightarrowx=?

$$\frac { 1 } { 1 - \frac { 1 } { 1 + \frac { 1 } { x } } } = 2 \Rightarrow x = ?$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

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

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

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}.

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

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

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

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

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

Combine like terms in x+1-x.

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

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

$$x+1=2$$

Subtract 1 from both sides.

$$x=2-1$$

Subtract 1 from 2 to get 1.

$$x=1$$