Solve =x/x+1+x-1/x=2.0

$$= \frac { x } { x + 1 } + \frac { x - 1 } { x } = 2.0$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

$$xx+\left(x+1\right)\left(x-1\right)=2x\left(x+1\right)$$

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

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

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

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

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

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

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

Subtract 2x^{2} from both sides.

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

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

$$-1=2x$$

Swap sides so that all variable terms are on the left hand side.

$$2x=-1$$

Divide both sides by 2.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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