SOLUTION: Appreciate help in solving a problem and checking the answer: ((6x-3)/x^2-x-12))-((2x-15)/x^2-x-12)) The answer I got is 4/(x-4) but not sure if this is correct and don't kno

Question 486610: Appreciate help in solving a problem and checking the answer:
((6x-3)/x^2-x-12))-((2x-15)/x^2-x-12))
The answer I got is 4/(x-4) but not sure if this is correct and don't know how to check.
Thanks much.
Diane
Found 2 solutions by mananth, chessace:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
Since () are used somewhat, assume (1st) this problem is
((6x-3)/x^2)-x-12-((2x-15)/x^2)-x-12 rather than
(2nd) (6x-3)/(x^2-x-12)-(2x-15)/(x^2-x-12).
Maybe it was clear in original form.
(1st):
((6x-3)/x^2)-x-12-((2x-15)/x^2)-x-12
= ((6x-3-2x+15)/x^2)-x-12-x-12
= ((4x+12)/x^2) -2(4x+12) not looking good!
(2nd):
(6x-3)/(x^2-x-12)-(2x-15)/(x^2-x-12)
= (6x-3-2x+15)/(x^2-x-12)
= (4x+12)/((x+3)(x-4))
= 4/(x-4)
Much better, and matches yours.
As for checking any answer, one quick test is to set x=0 then x=1 and see if results are same:
x=0: -3/(-12)-(-15)/(-12)= 1/4-5/4 = -1 v. -1 OK!
x=1: (3/-12)-(-13)/(-12) = -1/4 - 13/12 v. 4/(-3)
(-3/12)-13/12 v. -16/12 OK!
A 3rd point, say x=-1 would cinch it, but 2 is plenty.

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