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

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.
RELATED QUESTIONS
How do I turn .6% into a fraction? Everywhere I look for instructions it says .6 and out... (answered by macston,ikleyn)

I might not have the topic exactly right, but I have an issue. This assignment was due... (answered by josgarithmetic,Edwin McCravy,MathLover1,ikleyn)

One side of triangle has an equation of 2x - 5 next side has 3x + 20 and the last side... (answered by josgarithmetic)

Hi, I am doing a homework assignment and we are dealing with extraneous solutions. I am... (answered by solver91311)

This is calculus, and help would be very thanked. :) Filed under tests cuz I didn't... (answered by Alan3354)

How am i to get the solution to the equation |x-3|=2x+1? It says I am to end up with a... (answered by Alan3354,KMST,ankor@dixie-net.com)

I am not sure if this is a quadratic actually, but I wasn't sure what selection in the... (answered by RAY100,drj,Theo)

I need help with this equation please--Supposed to solve the equation and check for... (answered by profemmanuel2q@yahoo.com)

I dont know how to solve xDivided line x-1 equals 2x+10 divided line x+11 (answered by vidhyak)