<s>[INST] Solving a quadratic equation with parameters $$\frac { x+2 }{ a }- \frac { 2-a }{ x } =2$$
Steps I took:
$$\frac { x(x+2) }{ ax } -\frac { a(2-a) }{ ax } =\frac { 2ax }{ ax } $$
$$x^2+2x-2a+a^2=2ax$$
$$x^{ 2 }+2x-2a+a^{ 2 }-2ax=0$$
I get stuck at this point because I have no clue how to factor an equation in this form. Hints a more appreciated than the actual answer
 [/INST] $$x^2+(2-2a)x+a^2-2a=0$$
use the quadratic formula according to the following form
$$x^2+Ax+B=0$$
$$x=-0.5A\pm\sqrt{0.25A^2-B}$$
hence
$$x=(a-1)\pm\sqrt{(a-1)^2-a^2+2a}$$
$$x=(a-1)\pm\sqrt{a^2-2a+1-a^2+2a}$$
$$x=(a-1)\pm{1}$$
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