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

1 Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).