Solve A=2x-1/x+2

$$A = \frac{ 2x-1 }{ x+2 }$$

Solve for x

$$x=-\frac{2A+1}{A-2}$$

$$A\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by x+2.

$$A\left(x+2\right)=2x-1$$

Use the distributive property to multiply A by x+2.

$$Ax+2A=2x-1$$

Subtract 2x from both sides.

$$Ax+2A-2x=-1$$

Subtract 2A from both sides.

$$Ax-2x=-1-2A$$

Combine all terms containing x.

$$\left(A-2\right)x=-1-2A$$

The equation is in standard form.

$$\left(A-2\right)x=-2A-1$$

Divide both sides by A-2.

$$\frac{\left(A-2\right)x}{A-2}=\frac{-2A-1}{A-2}$$

Dividing by A-2 undoes the multiplication by A-2.

$$x=\frac{-2A-1}{A-2}$$

Divide -1-2A by A-2.

$$x=-\frac{2A+1}{A-2}$$

Variable x cannot be equal to -2.

$$x=-\frac{2A+1}{A-2}\text{, }x\neq -2$$

Solve for A

$$A=-\frac{1-2x}{x+2}$$

$$x\neq -2$$