SOLUTION: hello,can someone help me do a partial fraction decomposition on 19/15? I understand where the denominators come from 5*3 but the solution I got is 2/3+3/5 where did they come up

Question 1062410: hello,can someone help me do a partial fraction decomposition on 19/15? I understand where the denominators come from 5*3 but the solution I got is 2/3+3/5
where did they come up with the numerators I tried to use a system of equations equations but that didn't work.I could never produce the numerators 2 and 3. Thank you in advance!!!!
Found 2 solutions by rothauserc, KMST:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(19/15) = (9/15) + (10/15) = (3/5) + (2/3)
:

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Starting with a/3+b/5=19/15,
you get=5a+3b=19
You know that 3b is a multiple of 3.
You may realize that when you divide 19 by 3 you get a remainder of 1.
That tells you that if you divide 5a by 3 you would get 1 for a remainder.
With a=1, you get 5a=5, which divided by 3 gives you a remainder of 2.
With a=2, 5a=10, 10=9+1 divided by 3 gives you a remainder of 1,
so you know that a=2, with 5a=10, is a solution.
Then, 3b=19-5a=19-10=9, so b=9�3=3.
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