SOLUTION: I need to solve this equation and state any extraneous solutions. When it says over, it's a fraction. I didn't know how else to put it. a over 3a+6 minus a over 5a+10 equals 2

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Question 139405This question is from textbook Algebra 1
: I need to solve this equation and state any extraneous solutions. When it says over, it's a fraction. I didn't know how else to put it.
a over 3a+6
minus
a over 5a+10
equals 2 over 5
This question is from textbook Algebra 1

Answer by frostusna(7) (Show Source):
You can put this solution on YOUR website!
The equation form of your problem would look like this:

Since the two terms on the left hand side have different denominators they can't be subtracted as they are, therefor we must give them common denominators. We do that by multiplying each term's numerator and denominator by the denominator of the other term, esentially multiplying each term by the number 1. The equation becomes:

Multiplying out the numerators and denominators renders:

Now combining like terms in the numerator and multiplying each side by the denominator of the left hand term gives:

Or:
Now, subtract from each side and we end up with the quadratic equation:

Then, using the quadratic equation solver we get:

Solving this equation yields two solutions:
and . However, when the is substituted into the original equation you end up with 0 (zero) in both denominators, which makes the terms undefinable. So the one workable solution is .
I hope this helped.