Solve 4-2x/x=2x/3-x

$$\frac { 4 - 2 x } { x } = \frac { 2 x } { 3 - x }$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x,3-x.

$$\left(x-3\right)\left(4-2x\right)=-x\times 2x$$

Use the distributive property to multiply x-3 by 4-2x and combine like terms.

$$10x-2x^{2}-12=-x\times 2x$$

Multiply x and x to get x^{2}.

$$10x-2x^{2}-12=-x^{2}\times 2$$

Multiply -1 and 2 to get -2.

$$10x-2x^{2}-12=-2x^{2}$$

Add 2x^{2} to both sides.

$$10x-2x^{2}-12+2x^{2}=0$$

Combine -2x^{2} and 2x^{2} to get 0.

$$10x-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$10x=12$$

Divide both sides by 10.

$$x=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{5}$$