Solve ABB=r+1/r

$$A B B = \frac { r + 1 } { r }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{r+1}{rB^{2}}\text{, }&r\neq 0\text{ and }B\neq 0\\A\in \mathrm{C}\text{, }&B=0\text{ and }r=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r.

$$ABBr=r+1$$

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

$$AB^{2}r=r+1$$

The equation is in standard form.

$$rB^{2}A=r+1$$

Divide both sides by B^{2}r.

$$\frac{rB^{2}A}{rB^{2}}=\frac{r+1}{rB^{2}}$$

Dividing by B^{2}r undoes the multiplication by B^{2}r.

$$A=\frac{r+1}{rB^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{r+1}{rB^{2}}\text{, }&r\neq 0\text{ and }B\neq 0\\A\in \mathrm{R}\text{, }&B=0\text{ and }r=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r.

$$ABBr=r+1$$

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

$$AB^{2}r=r+1$$

The equation is in standard form.

$$rB^{2}A=r+1$$

Divide both sides by B^{2}r.

$$\frac{rB^{2}A}{rB^{2}}=\frac{r+1}{rB^{2}}$$

Dividing by B^{2}r undoes the multiplication by B^{2}r.

$$A=\frac{r+1}{rB^{2}}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\sqrt{\frac{r+1}{Ar}}\text{; }B=\sqrt{\frac{r+1}{Ar}}\text{, }&r\neq 0\text{ and }A\neq 0\\B\in \mathrm{C}\text{, }&A=0\text{ and }r=-1\end{matrix}\right.$$

Solve for B

$$\left\{\begin{matrix}B=\frac{\sqrt{A+\frac{A}{r}}}{A}\text{; }B=-\frac{\sqrt{A+\frac{A}{r}}}{A}\text{, }&\left(r\geq -1\text{ and }r<0\text{ and }A<0\right)\text{ or }\left(A>0\text{ and }r\leq -1\right)\text{ or }\left(r>0\text{ and }A>0\right)\\B\in \mathrm{R}\text{, }&A=0\text{ and }r=-1\end{matrix}\right.$$