SOLUTION: 3a-1/a^2+4a+4 - 3/a^2+2a = 3/a this is a problem from my homework that is asking me to simply solve the equation. i don't know where or how to start to get the correct answer of

Algebra ->  Linear-equations -> SOLUTION: 3a-1/a^2+4a+4 - 3/a^2+2a = 3/a this is a problem from my homework that is asking me to simply solve the equation. i don't know where or how to start to get the correct answer of       Log On


   

Question 11838: 3a-1/a^2+4a+4 - 3/a^2+2a = 3/a
this is a problem from my homework that is asking me to simply solve the equation. i don't know where or how to start to get the correct answer of
a = -9/8
any help with this would be greatly appreciated.
thanks
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i am assuming you mean %283a-1%29%2F%28a%5E2%2B4a%2B4%29+-+3%2F%28a%5E2%2B2a%29+=+3%2Fa? If so, then...

%283a-1%29%2F%28a%5E2%2B4a%2B4%29+-+3%2F%28a%5E2%2B2a%29+=+3%2Fa
%283a-1%29%2F%28%28a%2B2%29%28a%2B2%29%29+-+3%2F%28a%28a%2B2%29%29+=+3%2Fa

So, just fractions now...i will multiply both sides, that is ALL terms by the same thing, namely a(a+2)(a+2), as this is the lowest common factor of all three fractions. Doing this does not "change" the equation, it just "scales" it up a bit.

By multiplying each term by the above, we can then cancel the fractions to leave:

a%283a-1%29+-+3%28a%2B2%29+=+3%28a%2B2%29%28a%2B2%29
a%283a-1%29+-+3%28a%2B2%29+=+3%28a%5E2+%2B+4a+%2B+4%29
3a%5E2+-a+-+3a+-+6+=+3a%5E2+%2B+12a+%2B+12
3a%5E2+-4a+-+6+=+3a%5E2+%2B+12a+%2B+12
-4a+-+6+=+12a+%2B+12
-+6+=+16a+%2B+12
-18+=+16a
or 16a = -18
--> a = -18/16
--> a = -9/8

jon.