SOLUTION: Subtract 4x/x-5- 20/x-5 divide x2-36y^2/5x^2-30xy divided by (x^2+6xy)

Algebra ->  Equations -> SOLUTION: Subtract 4x/x-5- 20/x-5 divide x2-36y^2/5x^2-30xy divided by (x^2+6xy)      Log On


   

Question 121336: Subtract
4x/x-5-
20/x-5
divide
x2-36y^2/5x^2-30xy
divided by (x^2+6xy)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

4x%2F%28x-5%29-20%2F%28x-5%29 Start with the given expression


%284x-20%29%2F%28x-5%29 Since the denominators are equal, we can combine the fractions


%284%28x-5%29%29%2F%28x-5%29 Factor 4x-20 to get 4%28x-5%29



4cross%28%28x-5%29%29%2Fcross%28%28x-5%29%29 Cancel like terms


4 Simplify


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Answer:

So 4x%2F%28x-5%29-20%2F%28x-5%29 simplifies to 4. In other words 4x%2F%28x-5%29-20%2F%28x-5%29=4







#2


%28%28x%5E2-36y%5E2%29%2F%285x%5E2-30xy%29%29%2F%28%28x%5E2%2B6xy%29%2F1%29 Start with the given expression


%28%28x%5E2-36y%5E2%29%2F%285x%5E2-30xy%29%29%28%281%29%2F%28x%5E2%2B6xy%29%29 Multiply the first fraction by the reciprocal of the second fraction



%28%28%28x%2B6y%29%28x-6y%29%29%2F%285x%5E2-30xy%29%29%28%281%29%2F%28x%5E2%2B6xy%29%29 Factor x%5E2-36y%5E2 to get %28x%2B6y%29%28x-6y%29

%28%28%28x%2B6y%29%28x-6y%29%29%2F%285x%28x-6y%29%29%29%28%281%29%2F%28x%5E2%2B6xy%29%29 Factor 5x%5E2-30xy to get 5x%28x-6y%29

%28%28%28x%2B6y%29%28x-6y%29%29%2F%285x%28x-6y%29%29%29%28%281%29%2F%28x%28x%2B6y%29%29%29 Factor x%5E2%2B6xy to get x%28x%2B6y%29


%28x%2B6y%29%28x-6y%29%2F5x%28x-6y%29x%28x%2B6y%29 Combine the fractions



Cancel like terms



1%2F5x%5E2Simplify



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Answer:

So %28%28x%5E2-36y%5E2%29%2F%285x%5E2-30xy%29%29%2F%28%28x%5E2%2B6xy%29%2F1%29 simplifies to 1%2F5x%5E2. In other words %28%28x%5E2-36y%5E2%29%2F%285x%5E2-30xy%29%29%2F%28%28x%5E2%2B6xy%29%2F1%29=1%2F5x%5E2