Solve 2/x-1/frac{1-frac{1{10}}{10/x}}=2/x

$$\frac { \frac { 2 } { x - 1 } } { \frac { 1 - \frac { 1 } { 10 } } { \frac { 10 } { x } } } = \frac { 2 } { x }$$

Solve for x

$$x = \frac{109}{9} = 12\frac{1}{9} \approx 12.111111111$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{100}{9}\times \frac{2}{x-1}=2$$

Multiply \frac{100}{9} times \frac{2}{x-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{100\times 2}{9\left(x-1\right)}=2$$

Multiply 100 and 2 to get 200.

$$\frac{200}{9\left(x-1\right)}=2$$

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 9\left(x-1\right).

$$200=18\left(x-1\right)$$

Divide both sides by 18.

$$\frac{200}{18}=x-1$$

Reduce the fraction \frac{200}{18} to lowest terms by extracting and canceling out 2.

$$\frac{100}{9}=x-1$$

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

$$x-1=\frac{100}{9}$$

Add 1 to both sides.

$$x=\frac{100}{9}+1$$

Add \frac{100}{9} and 1 to get \frac{109}{9}.

$$x=\frac{109}{9}$$