SOLUTION: 3y+3 ----- 6y+12 divided by 18 ---- 5y+5 i need to simplify this and list any restrictions. please help! thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3y+3 ----- 6y+12 divided by 18 ---- 5y+5 i need to simplify this and list any restrictions. please help! thank you!      Log On


   

Question 178831: 3y+3
-----
6y+12
divided by
18
----
5y+5
i need to simplify this and list any restrictions. please help!
thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%283y%2B3%29%2F%286y%2B12%29%29%28%2818%29%2F%285y%2B5%29%29 Start with the given expression.


%28%283%28y%2B1%29%29%2F%286y%2B12%29%29%28%2818%29%2F%285y%2B5%29%29 Factor 3y%2B3 to get 3%28y%2B1%29.


%28%283%28y%2B1%29%29%2F%286%28y%2B2%29%29%29%28%2818%29%2F%285y%2B5%29%29 Factor 6y%2B12 to get 6%28y%2B2%29.


%28%283%28y%2B1%29%29%2F%286%28y%2B2%29%29%29%28%2818%29%2F%285%28y%2B1%29%29%29 Factor 5y%2B5 to get 5%28y%2B1%29.


%283%2A18%28y%2B1%29%29%2F%286%2A5%28y%2B2%29%28y%2B1%29%29 Combine the fractions.


%2854%28y%2B1%29%29%2F%2830%28y%2B2%29%28y%2B1%29%29 Multiply


%2854%2Ahighlight%28%28y%2B1%29%29%29%2F%2830%28y%2B2%29highlight%28%28y%2B1%29%29%29 Highlight the common terms.


%2854%2Across%28%28y%2B1%29%29%29%2F%2830%28y%2B2%29cross%28%28y%2B1%29%29%29 Cancel out the common terms.


54%2F%2830%28y%2B2%29%29 Simplify.


54%2F%2830y%2B60%29 Distribute


So %28%283y%2B3%29%2F%286y%2B12%29%29%28%2818%29%2F%285y%2B5%29%29 simplifies to 54%2F%2830y%2B60%29.


In other words, %28%283y%2B3%29%2F%286y%2B12%29%29%28%2818%29%2F%285y%2B5%29%29=54%2F%2830y%2B60%29 where y%3C%3E-2 or y%3C%3E-1 (these are the restrictions; we must take these values out of the domain since they cause a division by zero)