SOLUTION: I think I came up with the right answer, but would love for someone to double-check my work! The problem reads: Solve 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1 I came up with a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I think I came up with the right answer, but would love for someone to double-check my work! The problem reads: Solve 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1 I came up with a      Log On


   

Question 128558This question is from textbook Introductory Algebra
: I think I came up with the right answer, but would love for someone to double-check my work! The problem reads: Solve
3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1
I came up with a = -6 or -1 This question is from textbook Introductory Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's verify the solution a=-6



%283a-5%29%2F%28a%5E2%2B4a%2B3%29+%2B+%282a%2B2%29%2F%28a%2B3%29=%28a-3%29%2F%28a%2B1%29 Start with the given equation


Plug in a=-6. In other words, replace each a with -6



%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 Square and multiply


-23%2F15+%2B+10%2F3=9%2F5 Combine like terms


9%2F5=9%2F5 Combine the fractions on the right side and reduce


Since the two sides of the equation are equal, this verifies our answer.




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Let's verify the solution a=-1



%283a-5%29%2F%28a%5E2%2B4a%2B3%29+%2B+%282a%2B2%29%2F%28a%2B3%29=%28a-3%29%2F%28a%2B1%29 Start with the given equation


Plug in a=-1. In other words, replace each a with -1



%28-3-5%29%2F%281-4%2B3%29+%2B+%28-2%2B2%29%2F%28-1%2B3%29=%28-1-3%29%2F%28-1%2B1%29 Square and multiply


%28-8%29%2F%280%29+%2B+0%2F%282%29=%28-4%29%2F%280%29 Combine like terms



Notice how there are denominators of zero. Since division by zero is undefined, a=-1 is not a solution of the equation.




So our only solution is

a=-6