Expert: Paul Klarreich - 9/30/2009

Question
p(1+5x) = 6/(2-3x). What is p(x)?

Answer
Questioner: Jane
Country: United States
Category: Calculus
Private: No
Subject: Functions
Question: p(1+5x) = 6/(2-3x). What is p(x)?
...............................................

Suppose we let  u = 1 + 5x.

Then what is x?   u - 1 = 5x,  x = (u-1)/5
    6
--------------- =
2 - 3(u - 1)/5

     30
------------
10 - 3u + 3

  30
--------
13 - 3u
             30
so  p(u) = --------
          13 - 3u

WHICH MEANS (believe me) that:

          30
p(x) = --------
       13 - 3x

What's that, you say? You don't believe me?  Check it out:

              30
p(1 + 5x) = ------------
           13 - 3(1+5x)

              30
p(1 + 5x) = ------------
           13 - 3 - 15x

              30
p(1 + 5x) = --------
           10 - 15x

and you can reduce that and get ... guess what?

These things are indeed tricky.  The clue is that the 'x' in p(1 + 5x)  and
the 'x' in p(x) have nothing to do with each other.