Solve 2x/x+1-m+1/x^2+x=x+1/x

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

Solve for m

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

$$x\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x+1,x^{2}+x,x.

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

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

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

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

To find the opposite of m+1, find the opposite of each term.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

Subtract x^{2}\times 2 from both sides.

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

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

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

Add 1 to both sides.

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

Add 1 and 1 to get 2.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -x^{2}+2x+2 by -1.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\sqrt{m+3}+1\text{, }&\text{unconditionally}\\x=-\sqrt{m+3}+1\text{, }&m\neq 1\text{ and }m\neq -2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\sqrt{m+3}+1\text{, }&m\neq 1\text{ and }m\geq -3\text{ and }m\neq -2\\x=\sqrt{m+3}+1\text{, }&m\geq -3\end{matrix}\right.$$