SOLUTION: Please help me solve. {{{(3a-5)/(a^2+4a+3)}}}+{{{(2a+2)/(a+3)}}}={{{(a-3)/(a+1)}}} Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve. {{{(3a-5)/(a^2+4a+3)}}}+{{{(2a+2)/(a+3)}}}={{{(a-3)/(a+1)}}} Thank you.      Log On


   

Question 207635This question is from textbook Introductory Algebra
: Please help me solve.
%283a-5%29%2F%28a%5E2%2B4a%2B3%29+%282a%2B2%29%2F%28a%2B3%29=%28a-3%29%2F%28a%2B1%29
Thank you. This question is from textbook Introductory Algebra

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
%283a-5%29%2F%28a%5E2%2B4a%2B3%29%2B%282a%2B2%29%2F%28a%2B3%29=%28a-3%29%2F%28a%2B1%29
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%28a%5E2%2B4a%2B3%29 factors out to be %28a%2B3%29%2A%28a%2B1%29 so your equation becomes:

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if you multiply both sides of the equation by %28a%2B3%29%2A%28a%2B1%29 you will get:
%283a-5%29%2B%282a%2B2%29%2A%28a%2B1%29=%28a-3%29%28a%2B3%29
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if you simplify this you get:
%283a-5%29%2B2a%5E2+%2B+4a+%2B+2=a%5E2+-+9
if you subtract a%5E2+-+9 from both sides of the equation you get:
3a-5%2B2a%5E2+%2B+4a+%2B+2+-a%5E2+%2B+9=0
if you combine like terms you get:
a%5E2%2B7a%2B6=0
this factors out to be %28a%2B1%29%2A%28a%2B6%29+=+0
a+=+-1
or
a+=+-6
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when we substitute a = -1 in the original equation we get a division by 0 so a = -1 is no good.
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when we substitute a = -6 in the original equation we get (27) = (27) so a = -6 is good.
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computations for a = -6 are as follows:
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%283a-5%29%2F%28a%5E2%2B4a%2B3%29%2B%282a%2B2%29%2F%28a%2B3%29=%28a-3%29%2F%28a%2B1%29
becomes:
%28-18-5%29%2F%2836-24%2B3%29%2B%28-12%2B2%29%2F%28-6%2B3%29=%28-6-3%29%2F%28-6%2B1%29
which becomes:
%28-23%29%2F%2815%29%2B%28-10%29%2F%28-3%29=%28-9%29%2F%28-5%29
if we multiply both sides of the equation by 15 we get:
%28-23%29%2B%2850%29=%2827%29
%2827%29=%2827%29