Solve x+1/x^2+x+1-x-1/x^2-x+1=3/x(x^4+x^2+1)

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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 x\left(x^{2}+x+1\right)\left(x^{2}-x+1\right), the least common multiple of x^{2}+x+1,x^{2}-x+1,x\left(x^{4}+x^{2}+1\right).

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

Use the distributive property to multiply x by x^{2}-x+1.

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

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

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

Use the distributive property to multiply x by x^{2}+x+1.

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

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

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

To find the opposite of x^{4}-x, find the opposite of each term.

$$x^{4}+x-x^{4}+x=3$$

Combine x^{4} and -x^{4} to get 0.

$$x+x=3$$

Combine x and x to get 2x.

$$2x=3$$

Divide both sides by 2.

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