x+4×2-4+-2x-2×2-4

Combine the numerators over the common denominator.

x+4-2x-2×2-4

Subtract 2x from x.

-x+4-2×2-4

Subtract 2 from 4.

-x+2×2-4

-x+2×2-4

Rewrite 4 as 22.

-x+2×2-22

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=2.

-x+2(x+2)(x-2)

-x+2(x+2)(x-2)

Cancel the common factor of -x+2 and x-2.

Factor -1 out of -x.

-(x)+2(x+2)(x-2)

Rewrite 2 as -1(-2).

-(x)-1(-2)(x+2)(x-2)

Factor -1 out of -(x)-1(-2).

-(x-2)(x+2)(x-2)

Rewrite -(x-2) as -1(x-2).

-1(x-2)(x+2)(x-2)

Cancel the common factor.

-1(x-2)(x+2)(x-2)

Rewrite the expression.

-1x+2

-1x+2

Move the negative in front of the fraction.

-1x+2

-1x+2

Add (x+4)/(x^2-4)+(-2x-2)/(x^2-4)