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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve. (This one is really hard!) 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
%283a-5%29%2F%28a%5E2%2B4a%2B3%29 + %282a%2B2%29%2F%28a%2B3%29 = %28a-3%29%2F%28a%2B1%29
do some factoring here
%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29 + %282%28a%2B1%29%29%2F%28a%2B3%29 = %28a-3%29%2F%28a%2B1%29
The common denominator is (a+3)(a+1) multiply thru by this
:
(a+3)(a+1)*%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29 + (a+3)(a+1)*%282%28a%2B1%29%29%2F%28a%2B3%29 = (a+3)(a+1)*%28a-3%29%2F%28a%2B1%29
:
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
%283%28-6%29-5%29%2F%28%28-6%29%5E2%2B4%28-6%29%2B3%29 + %282%28-6%29%2B2%29%2F%28-6%2B3%29 = %28-6-3%29%2F%28-6%2B1%29
%28-23%29%2F%2836+-+24+%2B+3%29 + %28-10%29%2F%28-3%29 = %28-9%29%2F%28-5%29
%28-23%29%2F%2815%29 + %28-10%29%2F%28-3%29 = %28-9%29%2F%28-5%29
-23%2F%2815%29 + %2850%29%2F%2815%29 = %2827%29%2F%2815%29; confirms our solution
;
:
You can check it using x=-1