SOLUTION: 5y-20 ------ 3y+15 times 7y+35 ------ 10y+40 hi, i need to simplify this problem and find the restrictions if there are any. thank you!!

Algebra ->  Rational-functions -> SOLUTION: 5y-20 ------ 3y+15 times 7y+35 ------ 10y+40 hi, i need to simplify this problem and find the restrictions if there are any. thank you!!      Log On


   

Question 178821: 5y-20
------
3y+15
times
7y+35
------
10y+40

hi, i need to simplify this problem and find the restrictions if there are any.
thank you!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%285y-20%29%2F%283y%2B15%29%29%28%287y%2B35%29%2F%2810y%2B40%29%29 Start with the given expression.


%28%285%28y-4%29%29%2F%283y%2B15%29%29%28%287y%2B35%29%2F%2810y%2B40%29%29 Factor 5y-20 to get 5%28y-4%29.


%28%285%28y-4%29%29%2F%283%28y%2B5%29%29%29%28%287y%2B35%29%2F%2810y%2B40%29%29 Factor 3y%2B15 to get 3%28y%2B5%29.


%28%285%28y-4%29%29%2F%283%28y%2B5%29%29%29%28%287%28y%2B5%29%29%2F%2810y%2B40%29%29 Factor 7y%2B35 to get 7%28y%2B5%29.


%28%285%28y-4%29%29%2F%283%28y%2B5%29%29%29%28%287%28y%2B5%29%29%2F%2810%28y%2B4%29%29%29 Factor 10y%2B40 to get 10%28y%2B4%29.


%285%2A7%28y-4%29%28y%2B5%29%29%2F%283%2A10%28y%2B5%29%28y%2B4%29%29 Combine the fractions.


%2835%28y-4%29%28y%2B5%29%29%2F%2830%28y%2B5%29%28y%2B4%29%29 Multiply


Highlight the common terms.


%2835%28y-4%29cross%28%28y%2B5%29%29%29%2F%2830%2Across%28%28y%2B5%29%29%28y%2B4%29%29 Cancel out the common terms.


%2835%28y-4%29%29%2F%2830%28y%2B4%29%29 Simplify.


%2835y-140%29%2F%2830y%2B120%29 Distribute


So %28%285y-20%29%2F%283y%2B15%29%29%28%287y%2B35%29%2F%2810y%2B40%29%29 simplifies to %2835y-140%29%2F%2830y%2B120%29.


In other words, where y%3C%3E-5 or y%3C%3E-4 (these are the restrictions since these values will cause a division by zero)