Solve x-2-4/x-2=x*x-4/x-2

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

Solve for x

$$x\neq 2$$

Solution Steps

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

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

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

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

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

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

Combine -2x and -2x to get -4x.

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

Subtract 4 from 4 to get 0.

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

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

$$x^{2}-4x=x^{2}-4x$$

Subtract x^{2} from both sides.

$$x^{2}-4x-x^{2}=-4x$$

Combine x^{2} and -x^{2} to get 0.

$$-4x=-4x$$

Add 4x to both sides.

$$-4x+4x=0$$

Combine -4x and 4x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to 2.

$$x\in \mathrm{R}\setminus 2$$