Solve x-2/x-1/3=2/x

$$\frac { x - 2 } { x } - \frac { 1 } { 3 } = \frac { 2 } { x }$$

Solve for x

$$x=6$$

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 3x, the least common multiple of x,3.

$$3\left(x-2\right)+3x\left(-\frac{1}{3}\right)=3\times 2$$

Use the distributive property to multiply 3 by x-2.

$$3x-6+3x\left(-\frac{1}{3}\right)=3\times 2$$

Cancel out 3 and 3.

$$3x-6-x=3\times 2$$

Combine 3x and -x to get 2x.

$$2x-6=3\times 2$$

Multiply 3 and 2 to get 6.

$$2x-6=6$$

Add 6 to both sides.

$$2x=6+6$$

Add 6 and 6 to get 12.

$$2x=12$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x=6$$