SOLUTION: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus

Question 568486: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus sign is throwing me off. I know that the signs to the right of the minus sign change, but I'm having a little trouble with the combining. One of my problems is as follows:
2x-3/x+5-x^2-4x-19/x^2+8x+15

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use parentheses so you can see what you are doing.
-------------------
(2x-3)/(x+5)-(x^2-4x-19)/(x^2+8x+15)
----
Factor:
= (2x-3)/(x+5) - (x^2-4x-19)/[(x+5)(x+3)]
-----------------
LCD = (x+5)(x+3)
-----
Rewrite both factors with denominator = LCD
----
= [(x+3)(2x-3)]/LCD - [x^2-4x-19]/LCD
-------
Combine the numerators over the LCD:
---
= [2x^2+3x-9-x^2+4x+19]/LCD
----------------
Simplify:
= [x^2+7x+10]/LCD
----
Factor:
= [(x+5)(x+2)]/[(x+5)(x+3)]
----
Cancel the common factor:
= (x+2)/(x+3)
=======================
Cheers,
Stan H.
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