SOLUTION: 2/aČ-2a minus 3/aČ-a-2

Algebra ->  College  -> Linear Algebra -> SOLUTION: 2/aČ-2a minus 3/aČ-a-2      Log On


   

Question 119186: 2/aČ-2a minus 3/aČ-a-2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29
Whenever you subtract fractions, you need to have the same denominators.
Let's look at each denominator first.
D%5B1%5D=a%5E2-2a=a%28a-2%29
D%5B2%5D=a%5E2-a-2=%28a%2B1%29%28a-2%29
So if you multiply the first denominator by (a+1) and then second denominator by (a), they will have a common denominator of a(a+1)(a-2).
Remember whatever you multiply the denominator by, you also must multiply the numerator by.
2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=2%2F%28a%28a-2%29%29-3%2F%28%28a%2B1%29%28a-2%29%29

2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=%282%28a%2B1%29-3a%29%2F%28a%28a%2B1%29%28a-2%29%29
2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=%282a%2B2-3a%29%2F%28a%28a%2B1%29%28a-2%29%29
2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=%282-a%29%2F%28a%28a%2B1%29%28a-2%29%29
2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=%28-%28a-2%29%29%2F%28a%28a%2B1%29%28a-2%29%29

2%2F%28a%5E2-2a%29-3%2F%28a%5E2-a-2%29=%28-1%29%2F%28a%28a%2B1%29%29
Remember this relation only makes sense when a does not equal 0,-1,or 2.