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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

$$x\times 2=-4x+4+2x$$

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

$$x\times 2=-2x+4$$

Add 2x to both sides.

$$x\times 2+2x=4$$

Combine x\times 2 and 2x to get 4x.

$$4x=4$$

Divide both sides by 4.

$$x=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$x=1$$