Solve A=a-B+b/1-B

$$A = \frac { a - B + b } { 1 - B }$$

Solve for B

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

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.

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

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

$$-AB+A=a-B+b$$

Add B to both sides.

$$-AB+A+B=a+b$$

Subtract A from both sides.

$$-AB+B=a+b-A$$

Combine all terms containing B.

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

The equation is in standard form.

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

Divide both sides by -A+1.

$$\frac{\left(1-A\right)B}{1-A}=\frac{b+a-A}{1-A}$$

Dividing by -A+1 undoes the multiplication by -A+1.

$$B=\frac{b+a-A}{1-A}$$

Variable B cannot be equal to 1.

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

Solve for A

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

$$B\neq 1$$