RE: A math problem is driving me nuts!

On 5/8/04, Jim Roepcke said:

>It looks to me like it should be ((x2+5x)/(x+1))-3 > 0 instead. Can
>somebody please confirm this or explain how you might get from what I
>got to, to what he got to?

He did it right. Let's do it out the long way to see it.

1. x(x+5)
   ------ > 3
    x+1

Expand it to get:

2.  x^2      5x
   ----- + ----- > 3
    x+1     x+1

Subtract 3 from both sides to get:

3.  x^2      5x
   ----- + ----- - 3  > 0
    x+1     x+1

To begin the simplification, we need a common denominator, so multiple the 3 by (x+1)/(x+1)

4.  x^2      5x    3(x+1)
   ----- + ----- - ------  > 0
    x+1     x+1      x+1

Expand it to get:

5.  x^2      5x      3x     3*1
   ----- + ----- - ----- - ----- > 0
    x+1     x+1     x+1     x+1

Simplify it to get:

6.  x^2      2x      3
   ----- + ----- - -----  > 0
    x+1     x+1     x+1

Which is the same as:

7.  x^2 + 2x - 3
   --------------  > 0
         x+1

Got it?

Man, I'd forgotten how much I loved this stuff!

Seth