SOLUTION: The whole rational equations has me stumped! Can you please help with this one? Solve... 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1

Question 239034: The whole rational equations has me stumped! Can you please help with this one?
Solve...
3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1
Answer by College Student(505) (Show Source): You can put this solution on YOUR website!
Problem:

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It took me several steps to solve this problem. Look carefully as you move through the steps.
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First make eqn equal to zero:

Now factor first denominator:

I would also factor the second numerator. You'll know why in a moment... it'll make our lives easier.

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* In order to add fractions, we need common denominators, right?
* We also know that any number multiplied by 1 is equal to itself, in other words, it doesn't change the original value.
* Furthermore, we know that any number divided by itself is equal to 1, right?
* So, in order to have equal denominators, we need to multiply the second fraction by and the third denominator by .
* This is how the new equation would look like:
.

Now in a more cohesive way:

Since we now have the same denominator, we can group all numerators above one common denominator.

Now perform multiplications, leave denominator as is.

Distribute the negative sign in

Multiply the 2 in

Combine like terms:

Now in standard form to make it easier to factor:

Now simplify and you're done.

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It's a long problem. I hope you understood it and were able to follow it. :)
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