adding rational equations (ANSWER NEEDED ASAP)

Question

solve and find out what x can't be? answer needed ASAP

1/x+2 + 3/x^2-4

Answer 1

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/(x²-4)

 

The x²-4 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)/(x²-4)