x-4×2-2x+4×2-4

Factor x out of x2-2x.

Factor x out of x2.

x-4x⋅x-2x+4×2-4

Factor x out of -2x.

x-4x⋅x+x⋅-2+4×2-4

Factor x out of x⋅x+x⋅-2.

x-4x(x-2)+4×2-4

x-4x(x-2)+4×2-4

Simplify the denominator.

Rewrite 4 as 22.

x-4x(x-2)+4×2-22

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-4x(x-2)+4(x+2)(x-2)

x-4x(x-2)+4(x+2)(x-2)

x-4x(x-2)+4(x+2)(x-2)

To write x-4x(x-2) as a fraction with a common denominator, multiply by x+2x+2.

x-4x(x-2)⋅x+2x+2+4(x+2)(x-2)

To write 4(x+2)(x-2) as a fraction with a common denominator, multiply by xx.

x-4x(x-2)⋅x+2x+2+4(x+2)(x-2)⋅xx

Multiply x-4x(x-2) and x+2x+2.

(x-4)(x+2)x(x-2)(x+2)+4(x+2)(x-2)⋅xx

Multiply 4(x+2)(x-2) and xx.

(x-4)(x+2)x(x-2)(x+2)+4x(x+2)(x-2)x

Reorder the factors of x(x-2)(x+2).

(x-4)(x+2)x(x+2)(x-2)+4x(x+2)(x-2)x

Reorder the factors of (x+2)(x-2)x.

(x-4)(x+2)x(x+2)(x-2)+4xx(x+2)(x-2)

(x-4)(x+2)x(x+2)(x-2)+4xx(x+2)(x-2)

Combine the numerators over the common denominator.

(x-4)(x+2)+4xx(x+2)(x-2)

Expand (x-4)(x+2) using the FOIL Method.

Apply the distributive property.

x(x+2)-4(x+2)+4xx(x+2)(x-2)

Apply the distributive property.

x⋅x+x⋅2-4(x+2)+4xx(x+2)(x-2)

Apply the distributive property.

x⋅x+x⋅2-4x-4⋅2+4xx(x+2)(x-2)

x⋅x+x⋅2-4x-4⋅2+4xx(x+2)(x-2)

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅2-4x-4⋅2+4xx(x+2)(x-2)

Move 2 to the left of x.

x2+2⋅x-4x-4⋅2+4xx(x+2)(x-2)

Multiply -4 by 2.

x2+2x-4x-8+4xx(x+2)(x-2)

x2+2x-4x-8+4xx(x+2)(x-2)

Subtract 4x from 2x.

x2-2x-8+4xx(x+2)(x-2)

x2-2x-8+4xx(x+2)(x-2)

Add -2x and 4x.

x2+2x-8x(x+2)(x-2)

Factor x2+2x-8 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -8 and whose sum is 2.

-2,4

Write the factored form using these integers.

(x-2)(x+4)x(x+2)(x-2)

(x-2)(x+4)x(x+2)(x-2)

(x-2)(x+4)x(x+2)(x-2)

Cancel the common factor.

(x-2)(x+4)x(x+2)(x-2)

Rewrite the expression.

x+4x(x+2)

x+4x(x+2)

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