SOLUTION: It says, simplify the rational expression, state any excluded values 6xsqrt3 - 18xsqrt2 ___________ _______ 3xsqrt3 - 27x and also 3x-15 _____ 4x-20 I am really st

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: It says, simplify the rational expression, state any excluded values 6xsqrt3 - 18xsqrt2 ___________ _______ 3xsqrt3 - 27x and also 3x-15 _____ 4x-20 I am really st      Log On


   

Question 196762: It says, simplify the rational expression, state any excluded values
6xsqrt3 - 18xsqrt2
___________________
3xsqrt3 - 27x
and also
3x-15
_____
4x-20

I am really stuck, thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%286x%2Asqrt%283%29-18x%2Asqrt%282%29%29%2F%283x%2Asqrt%283%29-27x%29 Start with the given expression.


%286x%28sqrt%283%29-3%2Asqrt%282%29%29%29%2F%283x%2Asqrt%283%29-27x%29 Factor out the GCF 6x from the numerator.


%286x%28sqrt%283%29-3%2Asqrt%282%29%29%29%2F%283x%28sqrt%283%29-9%29%29 Factor out the GCF 3x from the denominator.


%283x%2A2%28sqrt%283%29-3%2Asqrt%282%29%29%29%2F%283x%28sqrt%283%29-9%29%29 Factor 6x into 3x%2A2


Highlight the common terms.


Cancel out the common terms.



%282%28sqrt%283%29-3%2Asqrt%282%29%29%29%2F%28sqrt%283%29-9%29 Simplify


%282%2Asqrt%283%29-6%2Asqrt%282%29%29%2F%28sqrt%283%29-9%29 Distribute


So
%286x%2Asqrt%283%29-18x%2Asqrt%282%29%29%2F%283x%2Asqrt%283%29-27x%29 simplifies to %282%2Asqrt%283%29-6%2Asqrt%282%29%29%2F%28sqrt%283%29-9%29


In other words, where x%3C%3E0





# 2




%283x-15%29%2F%284x-20%29 Start with the given expression.


%283%28x-5%29%29%2F%284x-20%29 Factor 3x-15 to get 3%28x-5%29.


%283%28x-5%29%29%2F%284%28x-5%29%29 Factor 4x-20 to get 4%28x-5%29.


%283%2Ahighlight%28%28x-5%29%29%29%2F%284%2Ahighlight%28%28x-5%29%29%29 Highlight the common terms.


%283%2Across%28%28x-5%29%29%29%2F%284%2Across%28%28x-5%29%29%29 Cancel out the common terms.


3%2F4 Simplify.


So %283x-15%29%2F%284x-20%29 simplifies to 3%2F4.


In other words, %283x-15%29%2F%284x-20%29=3%2F4 where x%3C%3E5.