Solve 4/x^2-8x+16=1/x-1/x-4

$$\frac { 4 } { x ^ { 2 } - 8 x + 16 } = \frac { 1 } { x } - \frac { 1 } { x - 4 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,4 since division by zero is not defined. Multiply both sides of the equation by x\left(x-4\right)^{2}, the least common multiple of x^{2}-8x+16,x,x-4.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x\times 4=x^{2}-8x+16-x\left(x-4\right)$$

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

$$x\times 4=x^{2}-8x+16-\left(x^{2}-4x\right)$$

To find the opposite of x^{2}-4x, find the opposite of each term.

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

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

$$x\times 4=-8x+16+4x$$

Combine -8x and 4x to get -4x.

$$x\times 4=-4x+16$$

Add 4x to both sides.

$$x\times 4+4x=16$$

Combine x\times 4 and 4x to get 8x.

$$8x=16$$

Divide both sides by 8.

$$x=\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x=2$$