Solve A=3-x/x-1

$$A = \frac { 3 - x } { x - 1 }$$

Solve for x

$$x=\frac{A+3}{A+1}$$

$$A\neq -1$$

Steps for Solving Linear Equation

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

$$A\left(x-1\right)=3-x$$

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

$$Ax-A=3-x$$

Add x to both sides.

$$Ax-A+x=3$$

Add A to both sides.

$$Ax+x=3+A$$

Combine all terms containing x.

$$\left(A+1\right)x=3+A$$

The equation is in standard form.

$$\left(A+1\right)x=A+3$$

Divide both sides by A+1.

$$\frac{\left(A+1\right)x}{A+1}=\frac{A+3}{A+1}$$

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

$$x=\frac{A+3}{A+1}$$

Variable x cannot be equal to 1.

$$x=\frac{A+3}{A+1}\text{, }x\neq 1$$

Solve for A

$$A=-\frac{x-3}{x-1}$$

$$x\neq 1$$