Philip P. answered • 06/10/18

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The rule for adding rational expressions is the same as the rule for adding fractions - you need to put them over a common denominator:

1/(x+2) + 3/(x

^{2}-4)The x

^{2}-4 is a difference of squares and factors to (x-2)(x+2):1/(x+2) + 3/(x-2)(x+2)

The common denominator is (x-2)(x+2). The second term is already over the common denominator. To put the first term over the common denominator, multiply it by (x-2)/(x-2):

1/(x+2) · (x-2)/(x-2) + 3/(x-2)(x+2)

(x-2)/(x-2)(x+2) + 3/(x-2)(x+2)

Now just add the numerators (over the CD):

(x-2+3)/(x-2)(x+2)

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

**(x+1)/(x**

^{2}-4)