Solve 4x-16/x^2-8x+16=4/x-4

$$\frac { 4 x - 16 } { x ^ { 2 } - 8 x + 16 } = \frac { 4 } { x - 4 }$$

Solve for x

$$x\neq 4$$

Solution Steps

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)^{2}, the least common multiple of x^{2}-8x+16,x-4.

$$4x-16=\left(x-4\right)\times 4$$

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

$$4x-16=4x-16$$

Subtract 4x from both sides.

$$4x-16-4x=-16$$

Combine 4x and -4x to get 0.

$$-16=-16$$

Compare -16 and -16.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to 4.

$$x\in \mathrm{R}\setminus 4$$