# Thread: Sums of rational functions

1. ## Sums of rational functions

I was hoping someone could help me out with this. Also, I was wondering if the steps could be numbered so I can refer back to a certain step just in case I get confused.. Ok.. here goes...

It says "Simplify"

3/(X^2+13x-14) + 3/(X^2+17x+42)
_____________________________
9/(x^2+17x+42) + 9/(x^2+x-6)

Thanks for any help. These rational functions are driving me mad..

2. Originally Posted by Mathfailure
I was hoping someone could help me out with this. Also, I was wondering if the steps could be numbered so I can refer back to a certain step just in case I get confused.. Ok.. here goes...

It says "Simplify"

3/(X^2+13x-14) + 3/(X^2+17x+42)
_____________________________
9/(x^2+17x+42) + 9/(x^2+x-6)

Thanks for any help. These rational functions are driving me mad..
Hi,

I've attached an image of my calculations. The best you can do with those "simplifactions" (to me it looks like the revenge of a sadist )is factoring the denominators as I've done:

3. Hello, Mathfailure!

Another approach . . .

Simplify:
. . . . . . . . 3 . . . . . . . . . . . . 3
. . . .----------------- .+ .-------------------
. . . . x² + 13x - 14 . . . .x² + 17x + 42
. . . ------------------------------------------
. . . . . . . . . 9 . . . . . . . . . . . .9
. . . . ------------------ . + . ------------
. . . . .x² + 17x + 42 . . . . x² + x - 6

. . . . . . . . . . . . .3 . . . . . . . . . . . 3
. . . . . . . .----------------- .+ .------------------
. . . . . . . .(x - 1)(x + 14) . . .(x + 3)(x + 14)
Factor: . -------------------------------------------
. . . . . . . . . . . . .9 . . . . . . . . . . . 9
. . . . . . . .------------------ .+ .----------------
. . . . . . . .(x + 3)(x + 14) . . .(x - 2)(x + 3)

Multiply top and bottom by the LCD: .(x - 1)(x - 2)(x + 3)(x + 14)

. . . .3(x - 2)(x + 3) + 3(x - 1)(x - 2)
. . . ---------------------------------------
. . . 9(x - 1)(x - 2) + 9(x - 1)(x + 14)

. . . . . . . 3(x - 2)·(x + 3 + x - 1) . . . . . .3(x - 2)(2x + 2)
Factor: . ------------------------------ . = . ---------------------
. . . . . . .9(x - 1)·(x - 2 + x + 14) . . . . .9(x - 1)(2x + 12)

. . . . . . . 3·2·(x - 2)(x + 1) . . . . .(x - 2)(x + 1)
Factor: . ---------------------- . = . ------------------ . . . . There!
. . . . . . . 9·2·(x - 1)(x + 6). . . . .3(x - 1)(x + 6)