SOLUTION: I do not know where to start and what to do to perform the proper operation to solve a rational expression. Please Help. {{{(6r^2+5rt-25t^2)/(6r^2+3rt-30t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I do not know where to start and what to do to perform the proper operation to solve a rational expression. Please Help. {{{(6r^2+5rt-25t^2)/(6r^2+3rt-30t      Log On


   

Question 271475: I do not know where to start and what to do to perform the proper operation to solve a rational expression. Please Help.

%286r%5E2%2B5rt-25t%5E2%29%2F%286r%5E2%2B3rt-30t%5E2%29
%289r%5E2-3rt-20t%5E2%29%2F%2821r%5E2-18rt-48t%5E2%29
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
6r^2+5rt-25t^2 / 6r^2+3rt-30t^2
Factor where you can:
[6r^2+15rt-10rt-25t^2] / [6r^2+15rt-12rt-30t^2]
---
[3r(2r+5t)-5t(2r+5t)] / [3r(2r+5t)-6t(2r+5t)]
---
[(2r+5t)(3r-5t)] / [(2r+5t)(3r-6t)]
Cancel the 2r+5t factor:
Ans: (3r-5t)/(3r-6t)
=================================
Follow the same procedure for the 2nd problem.
Cheers,
Stan H.




9r^2-3rt-20t^2 / 21r^2-18rt-48t^2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
    %286r%5E2%2B5rt-25t%5E2%29%2F%286r%5E2%2B3rt-30t%5E2%29  

Factor the numerator

   6r%5E2%2B5rt-25t%5E2
   %283r-5%29%282r%2B5%29

Factor the denominator:

   6r%5E2%2B3rt-30t%5E2
   3%282r%5E2%2Brt-10t%5E2%29
   3%28r-2%29%282r%2B5%29

Now write the factored numerator on top and
the factored denominator on the bottom:

   %28%283r-5t%29%282r%2B5t%29%29%2F%283%28r-2t%29%282r%2B5t%29%29

The %282r%2B5t%29's will cancel:

   %28%283r-5t%29%28cross%282r%2B5t%29%29%29%2F%283%28r-22%29%28cross%282r%2B52%29%29%29

   %283r-5t%29%2F%283%28r-2t%29%29   

-------------------------------------

 %289r%5E2-3rt-20t%5E2%29%2F%2821r%5E2-18rt-48t%5E2%29

Factor the numerator

   9r%5E2-3rt-20t%5E2
   %283r-5t%29%283r%2B4t%29

Factor the denominator:

   21r%5E2-18rt-48t%5E2
   3%287r%5E2-6rt-16t%5E2%29
   3%28r-2t%29%287r%2B8t%29

Now write the factored numerator on top and
the factored denominator on the bottom:

   %28%283r-5t%29%283r%2B4t%29%29%2F%283%28r-2t%29%287r%2B8t%29%29

Nothing cancels so you can go no further.

Edwin