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

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 3x-1=xx-2\times 1$$

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

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

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

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

Multiply 2 and 1 to get 2.

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

Subtract x^{2} from both sides.

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

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

$$2x^{2}-1=-2$$

Add 1 to both sides.

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

Add -2 and 1 to get -1.

$$2x^{2}=-1$$

Divide both sides by 2.

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

The equation is now solved.

$$x=\frac{\sqrt{2}i}{2} x=-\frac{\sqrt{2}i}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 3x-1=xx-2\times 1$$

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

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

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

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

Multiply 2 and 1 to get 2.

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

Subtract x^{2} from both sides.

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

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

$$2x^{2}-1=-2$$

Add 2 to both sides.

$$2x^{2}-1+2=0$$

Add -1 and 2 to get 1.

$$2x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8}}{2\times 2}$$

Take the square root of -8.

$$x=\frac{0±2\sqrt{2}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{2}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{4} when ± is plus.

$$x=\frac{\sqrt{2}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{4} when ± is minus.

$$x=-\frac{\sqrt{2}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{2}i}{2} x=-\frac{\sqrt{2}i}{2}$$