Solve A=2b/B-1

$$A = \frac { 2 b } { B - 1 }$$

Solve for B

$$\left\{\begin{matrix}B=\frac{A+2b}{A}\text{, }&b\neq 0\text{ and }A\neq 0\\B\neq 1\text{, }&A=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable B cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by B-1.

$$A\left(B-1\right)=2b$$

Use the distributive property to multiply A by B-1.

$$AB-A=2b$$

Add A to both sides.

$$AB=2b+A$$

The equation is in standard form.

$$AB=A+2b$$

Divide both sides by A.

$$\frac{AB}{A}=\frac{A+2b}{A}$$

Dividing by A undoes the multiplication by A.

$$B=\frac{A+2b}{A}$$

Variable B cannot be equal to 1.

$$B=\frac{A+2b}{A}\text{, }B\neq 1$$

Solve for A

$$A=\frac{2b}{B-1}$$

$$B\neq 1$$