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..
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)