Need help with hw-adding fractions with letters?

Question

Here it is

9x
------
(x+7)(x-7)

Plus

x
------
(x-7)
I know that you have to get the bottom the same but what do I do with that (x+7)? I think it has to do with the recipricol thing but not sure

Your help will be of thanx

Answer 1

9x x
------ + _____
(x+7)(x-7) x-7

Okay, now you need to have a common denominator. Multiply both the top and bottom of the 2nd fraction by (x+7) and it will be ready to add to the first

9x x (x+7)
------ + _____
(x+7)(x-7) (x-7)(x+7)

9x+x(x+7)
------------- now it's combined, see?
(x-7)(x+7)

xsquared + 7x+9x <--- make it simpler
------------------------
(x-7)(x+7)


xsquared + 16x
-------------------- <-- simpler still
xsquared - 49

Answer 2

LCD = (x+7)(x-7)
just as with all fractions you need to find an LCD and have a least common multiple

multiply the second fraction by (x+7)/(x+7) to make the denominators common
= 9x/(x+7)(x-7) + x(x+7)/(x+7)(x-7)
= x^2+9x+7x/(x+7)(x-7)
= x^2+16x/(x+7)(x-7)
= x^2+16x/x^2-49 ~ special products
= -16x/49 ~ simplify

p.s.- the letters are called variables. in this case polynomials, or special products (sum of two terms) specifically