Solve x+2a/x-2=3

$$\frac { x + 2 a } { x - 2 } = 3$$

Solve for a

$$a=x-3$$

$$x\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$x+2a=3\left(x-2\right)$$

Use the distributive property to multiply 3 by x-2.

$$x+2a=3x-6$$

Subtract x from both sides.

$$2a=3x-6-x$$

Combine 3x and -x to get 2x.

$$2a=2x-6$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{2x-6}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{2x-6}{2}$$

Divide -6+2x by 2.

$$a=x-3$$

Solve for x

$$x=a+3$$

$$a\neq -1$$

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.

$$x+2a=3\left(x-2\right)$$

Use the distributive property to multiply 3 by x-2.

$$x+2a=3x-6$$

Subtract 3x from both sides.

$$x+2a-3x=-6$$

Combine x and -3x to get -2x.

$$-2x+2a=-6$$

Subtract 2a from both sides.

$$-2x=-6-2a$$

The equation is in standard form.

$$-2x=-2a-6$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{-2a-6}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{-2a-6}{-2}$$

Divide -6-2a by -2.

$$x=a+3$$

Variable x cannot be equal to 2.

$$x=a+3\text{, }x\neq 2$$