SOLUTION: 3y/4y-20+9y/6y-30 this is the problem i can't figure out...it says add or subtract as indicated. simplify the result if possible. i have figured out the other porblems yet i am

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3y/4y-20+9y/6y-30 this is the problem i can't figure out...it says add or subtract as indicated. simplify the result if possible. i have figured out the other porblems yet i am      Log On


   

Question 178902This question is from textbook ALGEBRA BLITZER 3RD EDITION
: 3y/4y-20+9y/6y-30 this is the problem i can't figure out...it says add or subtract as indicated. simplify the result if possible. i have figured out the other porblems yet i am stumped on this one. the book answer says 9y/4(y-5)
i have contemplated this over and over yet can not see how they got this answer.
thank you for your time. This question is from textbook ALGEBRA BLITZER 3RD EDITION

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can factor both denominators,
3y%2F%284y-20%29%2B9y%2F%286y-30%29=3y%2F%284%28y-5%29%29%2B9y%2F%286%28y-5%29%29
3y%2F%284y-20%29%2B9y%2F%286y-30%29=%283y%2F4%29%2F%28y-5%29%2B%289y%2F6%29%2F%28y-5%29
Since they have the same denominator, we can just add numerators,
3y%2F%284y-20%29%2B9y%2F%286y-30%29=%28%283y%2F4%29%2B%289y%2F6%29%29%2F%28y-5%29
Let's focus on the numerator only and simplify it,
%283y%2F4%29%2B%289y%2F6%29=%283%2F3%29%283y%2F4%29%2B%282%2F2%29%289y%2F6%29
%283y%2F4%29%2B%289y%2F6%29=%289y%2F12%29%2B%2818y%2F12%29
%283y%2F4%29%2B%289y%2F6%29=%289y%2B18y%29%2F12%29
%283y%2F4%29%2B%289y%2F6%29=%2827y%29%2F12%29
%283y%2F4%29%2B%289y%2F6%29=%289y%29%2F4%29
Now we replace that in the numerator,
3y%2F%284y-20%29%2B9y%2F%286y-30%29=%28%283y%2F4%29%2B%289y%2F6%29%29%2F%28y-5%29
3y%2F%284y-20%29%2B9y%2F%286y-30%29=%289y%2F4%29%2F%28y-5%29
3y%2F%284y-20%29%2B9y%2F%286y-30%29=9y%2F%284%28y-5%29%29