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

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

Solve for x

$$x=\frac{1}{7}\approx 0.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right), the least common multiple of 3,x-1.

$$\left(x-1\right)\left(3x-1\right)-3\times 2x=x\times 3\left(x-1\right)$$

Use the distributive property to multiply x-1 by 3x-1 and combine like terms.

$$3x^{2}-4x+1-3\times 2x=x\times 3\left(x-1\right)$$

Multiply -3 and 2 to get -6.

$$3x^{2}-4x+1-6x=x\times 3\left(x-1\right)$$

Combine -4x and -6x to get -10x.

$$3x^{2}-10x+1=x\times 3\left(x-1\right)$$

Use the distributive property to multiply x\times 3 by x-1.

$$3x^{2}-10x+1=3x^{2}-x\times 3$$

Multiply -1 and 3 to get -3.

$$3x^{2}-10x+1=3x^{2}-3x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-10x+1-3x^{2}=-3x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-10x+1=-3x$$

Add 3x to both sides.

$$-10x+1+3x=0$$

Combine -10x and 3x to get -7x.

$$-7x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-7x=-1$$

Divide both sides by -7.

$$x=\frac{-1}{-7}$$

Fraction \frac{-1}{-7} can be simplified to \frac{1}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{7}$$