12/x+2+8/x-2=4


Since you're adding two fractions, get a common denominator. In this case, our common denominator would be (x+2)(x-2). So,

12(x-2)/(x+2)(x-2)+8(x+2)/(x-2)(x+2)=4

Now just simply add the fractions since they have common denominators.

12x-24+8x+16/x^2-4 Note: (x+2)(x-2)=x^2-4 because of the difference of two squares.

20x-8=4(x^2-4)

20x-8=4x^2-16

20x=4x^2-8

4x^2-20x-8=0

Use the quadratic formula: -b+/- sqrt(b^2-4ac)/2a

4x^2-20x-8 is in the form ax^2+bx+c

-(-20)+/-sqrt((-20)^(2)-4(4)(-8))/8

20+/-sqrt(400+128)/8

20+/-sqrt(528)/8

so x=20+sqrt(528)/8 or x=20-sqrt(528)/8