SOLUTION: I am not sure on how to find the common denomenator correctly for this problem any help would be appreciated. y/y+1 - 2y/y+2

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Question 62094: I am not sure on how to find the common denomenator correctly for this problem any help would be appreciated.
y/y+1 - 2y/y+2
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(48569) About Me  (Show Source):
You can put this solution on YOUR website!
y/(y+1) - 2y/(y+2)
The least common denominator (LCD) is (y+1)(y+2)
= y(y+2)/LCD - 2y(y+1)/LCD
= [y^2+2y-(2y^2+2y)]/LCD
=[-y^2]/LCD
=-y^2/[y+1)(y+2)]
Cheers,
Stan H.

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
When adding or subtraction fractions with different denominators, you can always find their common denominator by multiplying the denominators. The resulting common denominator may not be the lowest common denominator (LCD) but it will allow to add/subtract the fractions.
y%2F%28y%2B1%29+-+2y%2F%28y%2B2%29
Multiply the top & bottom of the first fraction by the denominator of the second and multiply the top & bottom of the second fraction by the denominator of the first.
y%28y%2B2%29%2F%28%28y%2B1%29%28y%2B2%29%29+-+2y%28y%2B1%29%2F%28%28y%2B1%29%28y%2B2%29%29 Simplifying this:
%28%28y%5E2%2B2y%29-%282y%5E2%2B2y%29%29%2F%28y%5E2%2B3y%2B2%29 Simplifying further:
%28y%5E2%2B2y-2y%5E2-2y%29%2F%28y%5E2%2B3y%2B2%29 Simplifying even further:
-y%5E2%2F%28y%5E2%2B3y%2B2%29