Solve m=2(x+2)/x-2(x-2)

$$m = \frac { 2 ( x + 2 ) } { x - 2 ( x - 2 ) }$$

Solve for x

$$x=-\frac{4\left(1-m\right)}{m+2}$$

$$m\neq -2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -x+4.

$$m\left(-x+4\right)=2\left(x+2\right)$$

Use the distributive property to multiply m by -x+4.

$$-mx+4m=2\left(x+2\right)$$

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

$$-mx+4m=2x+4$$

Subtract 2x from both sides.

$$-mx+4m-2x=4$$

Subtract 4m from both sides.

$$-mx-2x=4-4m$$

Combine all terms containing x.

$$\left(-m-2\right)x=4-4m$$

Divide both sides by -m-2.

$$\frac{\left(-m-2\right)x}{-m-2}=\frac{4-4m}{-m-2}$$

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

$$x=\frac{4-4m}{-m-2}$$

Divide 4-4m by -m-2.

$$x=-\frac{4\left(1-m\right)}{m+2}$$

Variable x cannot be equal to 4.

$$x=-\frac{4\left(1-m\right)}{m+2}\text{, }x\neq 4$$

Solve for m

$$m=\frac{2\left(x+2\right)}{4-x}$$

$$x\neq 4$$