Solve (2/x)-(1/frac{x{4-x}})=1/3

$$( \frac{ 2 }{ x } )-( \frac{ 1 }{ \frac{ x }{ 4-x } } )= \frac{ 1 }{ 3 }$$

Solve for x

$$x=3$$

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.

$$3\times 2-\left(12-3x\right)=x$$

Multiply 3 and 2 to get 6.

$$6-\left(12-3x\right)=x$$

To find the opposite of 12-3x, find the opposite of each term.

$$6-12+3x=x$$

Subtract 12 from 6 to get -6.

$$-6+3x=x$$

Subtract x from both sides.

$$-6+3x-x=0$$

Combine 3x and -x to get 2x.

$$-6+2x=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$2x=6$$

Divide both sides by 2.

$$x=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x=3$$