Find the equation for the slant asymptote for f(x) = (x^2 + 2x)/(7x- 35)

Question

amistre64 · Answer

thats just long division....

amistre64 · Answer

(1/7)x +1
             -----------
7x- 35 | x^2   +2x
           - x^2    +5x
          -------------
                           7x +0
                         -7x +35
                        ---------
                                  35 <- remainder


                      35
x/7 + 1 + ------- <-- the remainder her gets canceled
                  7x-35

the oblique asymptote should be:

(1/7)x +1

anonymous · Answer

That makes sense, but I have a question about the long division. Shouldnt the 2x in the first row subtract the 5x underneath it to get -3x instead of add to get 7x?

amistre64 · Answer

No, remember how to do long division with actual numbers...

we find the value we are looking for and then "subtract" that value from our problem, like this:

       2      <- 2(5) = 10  so we "subtract" that value from "13"
   -------
5 |132
   -10
   -----
       3

same setup, same rules apply.

amistre64 · Answer

since : (1/7)x times (-35) = -5x ; we "subtract" -5x from the answer.

+2x -(-5x) = 2x + 5x = 7x