Solve -b(x^2+1)/(x^2-1)^2=0

$$\frac { - b ( x ^ { 2 } + 1 ) } { ( x ^ { 2 } - 1 ) ^ { 2 } } = 0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=0\text{, }&x\neq -1\text{ and }x\neq 1\\b\in \mathrm{C}\text{, }&x=-i\text{ or }x=i\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-b\right)\left(x^{2}+1\right)=0$$

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

$$\left(-b\right)x^{2}-b=0$$

Reorder the terms.

$$-bx^{2}-b=0$$

Combine all terms containing b.

$$\left(-x^{2}-1\right)b=0$$

Divide 0 by -x^{2}-1.

$$b=0$$

Solve for b

$$b=0$$

$$|x|\neq 1$$

Steps for Solving Linear Equation

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

$$\left(-b\right)\left(x^{2}+1\right)=0$$

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

$$\left(-b\right)x^{2}-b=0$$

Reorder the terms.

$$-bx^{2}-b=0$$

Combine all terms containing b.

$$\left(-x^{2}-1\right)b=0$$

Divide 0 by -x^{2}-1.

$$b=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-i\text{; }x=i\text{, }&\text{unconditionally}\\x\in \mathrm{C}\setminus -1,1\text{, }&b=0\end{matrix}\right.$$

Solve for x

$$x\in \mathrm{R}\setminus 1,-1$$

$$b=0$$