SOLUTION: (3a-5)/(a^2+4a+3)+(2a+2)/(a+3)=(a-3)/(a+1)

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Question 168278This question is from textbook Introductory Algebra
: (3a-5)/(a^2+4a+3)+(2a+2)/(a+3)=(a-3)/(a+1)
This question is from textbook Introductory Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28%283a-5%29%29%2F%28%28a%5E2%2B4a%2B3%29%29 + %28%282a%2B2%29%29%2F%28%28a%2B3%29%29 = %28%28a-3%29%29%2F%28%28a%2B1%29%29
:
Factor where we can:
%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29 + %282%28a%2B1%29%29%2F%28%28a%2B3%29%29 = %28%28a-3%29%29%2F%28%28a%2B1%29%29
:
Multiply equation by (a+3)(x+1)
(a+3)(a+1)*%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29 + (a+3)(a+1)*%282%28a%2B1%29%29%2F%28%28a%2B3%29%29 = (a+3)(a+1)*%28%28a-3%29%29%2F%28%28a%2B1%29%29
:
Cancel out the denominators and you have:
(3a-5) + 2(a+1)(a+1) = (a+3)(a-3)
:
FOIL
(3a - 5) + 2(a^2 + 2a + 1) = a^2 - 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 this to:
(a + 6)(a + 1) = 0
:
a = -6
and
a = -1
:
Check solution of x=-6 in original equation
%28%283%28-6%29-5%29%29%2F%28%28-6%5E2%2B4%28-6%29%2B3%29%29 + %28%282%28-6%29%2B2%29%29%2F%28%28-6%2B3%29%29 = %28%28-6-3%29%29%2F%28%28-6%2B1%29%29
Do the math, find the common denominator, and you have;
-23%2F15 + 50%2F15 = 27%2F15
:
x=-1 can not be a solution, note that in the last denominator we have division by 0