SOLUTION: add or subtract as indicated. Simplify if possible: 3y/4y-20+9y/6y-30 Please help!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: add or subtract as indicated. Simplify if possible: 3y/4y-20+9y/6y-30 Please help!!      Log On


   

Question 183372This question is from textbook
: add or subtract as indicated. Simplify if possible:
3y/4y-20+9y/6y-30
Please help!! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3y%2F%284y-20%29%2B9y%2F%286y-30%29 Start with the given expression


3y%2F%284%28y-5%29%29%2B9y%2F%286y-30%29 Factor 4y-20 to get 4%28y-5%29


3y%2F%284%28y-5%29%29%2B9y%2F%286%28y-5%29%29 Factor 6y-30 to get 6%28y-5%29


Notice how the LCM (or LCD) is 24%28y-5%29 (note: most often, you can find the LCD by multiplying the denominators and removing any repeated terms)


So the goal is to get EVERY denominator equal to the LCD


%286%2A3y%29%2F%286%2A4%28y-5%29%29%2B9y%2F%286%28y-5%29%29 Multiply the first fraction by 6%2F6


%2818y%29%2F%2824%28y-5%29%29%2B9y%2F%286%28y-5%29%29 Multiply


%2818y%29%2F%2824%28y-5%29%29%2B%284%2A9y%29%2F%284%2A6%28y-5%29%29 Multiply the second fraction by 4%2F4


%2818y%29%2F%2824%28y-5%29%29%2B%2836y%29%2F%2824%28y-5%29%29 Multiply



Now that the denominators are equal, we can combine them:


%2818y%2B36y%29%2F%2824%28y-5%29%29 Add the fractions


%2854y%29%2F%2824%28y-5%29%29 Combine like terms.


%289y%29%2F%284%28y-5%29%29 Reduce 54%2F24 to get 9%2F4


%289y%29%2F%284y-20%29 Distribute



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Answer:


So 3y%2F%284y-20%29%2B9y%2F%286y-30%29 simplifies to %289y%29%2F%284y-20%29



In other words, 3y%2F%284y-20%29%2B9y%2F%286y-30%29=%289y%29%2F%284y-20%29 where y%3C%3E5