Simplify the expression 2x/(x^2-4)+5/(x-2)

We notice that the denominator of the 1st fraction is a
difference of 2 squares that will return the product:

a^2 -
b^2 = (a-b)(a+b)

x^2 - 4 =
(x-2)(x+2)

The expression to be simplified will
become:

2x/(x-2)(x+2) +
5/(x-2)

The fractions cannot be added since they do not
have the same denominator, therefore we'll create the same denominator to
both.

For this reason, we must multiply the 2nd fraction by
(x+2) to get the same denominator as the one of the 1st
fraction.

2x/(x-2)(x+2) + 5(x+2)/(x-2)(x+2) = [2x +
5(x+2)]/(x-2)(x+2)

We'll combine like terms inside
brackets:

2x/(x-2)(x+2) + 5(x+2)/(x-2)(x+2) =
(7x+10)/(x-2)(x+2)

The simplified from of the
given expression is: (7x+10)/(x^2 - 4).