SOLUTION: Solve. (This one is really hard!) 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1

Question 241131: Solve. (This one is really hard!)
3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
+ =
do some factoring here
+ =
The common denominator is (a+3)(a+1) multiply thru by this
:
(a+3)(a+1)* + (a+3)(a+1)* = (a+3)(a+1)*
:
Cancel out the denominators, leaving:
(3a - 5) + (a+1)*2(a+1) = (a+3)(a-3)
:
FOIL
3a - 5 + 2(a^2 + 2a+ 1) = a^2 + 3a - 3a - 9
:
3a - 5 + 2a^2 + 4a + 2 = a^2 - 9
:
combine like terms on the left
2a^2 - a^2 + 3a + 4a - 5 + 2 + 9 = 0
:
a^2 + 7a + 6 = 0
Factor
(a + 6)(a + 1) = 0
Two solutions
a = -6
a = -1
;
:
Check in original equation using x=-6
+ =
+ =
+ =
+ = ; confirms our solution
;
:
You can check it using x=-1
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