simplify expression?

Question

a
_____
a^2 - a

+

a
______
a^2 + a

I'm not sure if there's some formula that I'm supposed to use.

Answer 1

It should say:

2a
_____
(a^2-1)

Answer 2

im not entirely sure, but this is what i got...
a/a^2 -a + a/a^2+a= a/a(a-1) + a/a(a+1)...the denominators both have an a in common, so you can factor that out (whats left from factoring is in the parenthesis). then you can cancel the a's, so ur left with 1/a-1+1/a+1. The denominators must be the same in order to add..so u must find a common denominator which is a^2-1 ( you multiply the denominators together to get the common denominator. For the first fraction, in order to get a^2-1 on the bottom, u must multiply 1/a-1 by a+1 and u get a+1/a^2-1. then u do the same for the second fraction, but u multiply with a-1 in order to get a^2-1, which goes like this: 1/a+1 times a-1= a-1/a^2-1. Now that the denominators are the same, u can add across. so a-1+a+1/a^2-1=2a/a^2-1. hopefully u understand all of this, if not, im sorry that i made it confusing for you. good luck!!

Answer 3

No special formula here, I guess, you can begin by dividing both enumerators and denominators by a, getting (for a != 0)
1/(a-1) + 1/(a+1)
then you find the common denominator, (a-1)*(a+1), or (a^2-1)
and add the fractions, getting 2a/(a^2 -1)

Answer 4

dont rely on formulas , use your common sense

you can divide away the a
1/a-1
+
1/a+1

if you dont find this simple enough
you can put them in another form you like

Answer 5

a+a^3?

Not sure, math is not my strong suite! Good luck!