Question 482500
obviously we need to add these fractions that have unlike denominators, so what we need to do is find the LCD


f(x)= ((x+8)/(x-9))+((5x-4)/(x+2))


Now, what would be our common denominator?
It would be (x-9)(x+2)

Now we multiply the top and bottom of the first fraction by (x+2)

Then the top and bottom of the second fraction is multiplied by (x-9)

this gives us:

(x+2)(x+8)       (x-9)(5x-4)
----------  +   -------------
(x-9)(x+2)       (x-9)(x+2)


Now we combine the fractions and get 

  (x+2)(x+8)+(x-9)(5x-4)
----------------------------     
         (x-9)(x+2)

Now lets expand the numerator of this fraction. We can use Foil for this.

  (x^2+10x+16)+(5x^2-49x+36)
-----------------------------
     (x-9)(x+2)

Our last step is to combine like terms in the numerator. 

      
      6x^2-39x+52
     --------------
       (x-9)(x+2)


Voila! That is our answer.