Solve 1+2x/x-6x/3x-1+4/x-3x^2=0

$$\frac { 1 + 2 x } { x } - \frac { 6 x } { 3 x - 1 } + \frac { 4 } { x - 3 x ^ { 2 } } = 0$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by x\left(3x-1\right), the least common multiple of x,3x-1,x-3x^{2}.

$$\left(3x-1\right)\left(1+2x\right)-x\times 6x-4=0$$

Use the distributive property to multiply 3x-1 by 1+2x and combine like terms.

$$x+6x^{2}-1-x\times 6x-4=0$$

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

$$x+6x^{2}-1-x^{2}\times 6-4=0$$

Subtract 4 from -1 to get -5.

$$x+6x^{2}-5-x^{2}\times 6=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$x+6x^{2}-x^{2}\times 6=5$$

Multiply -1 and 6 to get -6.

$$x+6x^{2}-6x^{2}=5$$

Combine 6x^{2} and -6x^{2} to get 0.

$$x=5$$