SOLUTION: Can I please get help dividing this? I tried it a few times and keep getting confused. x^3+125/x^3-125 divided by x^2-5x+25/x-5

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Can I please get help dividing this? I tried it a few times and keep getting confused. x^3+125/x^3-125 divided by x^2-5x+25/x-5      Log On


   

Question 171490: Can I please get help dividing this? I tried it a few times and keep getting confused.
x^3+125/x^3-125 divided by x^2-5x+25/x-5
Found 2 solutions by Mathtut, monika_p:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
first lets invert and multiply..(we are inverting the%28x%5E2-5x%2B25%29%2F%28x-5%29term
:
lets factor certain terms such as the sum of cubes and the difference of cubes
:
x%5E3%2B5%5E3=(x+5)(x^2-5x+25)
:
x%5E3-5%5E3=(x+5)(x^2+5x+25)...with that info lets begin
:

:
highlight%28%28x%2B5%29%2F%28x%5E2%2B5x%2B25%29%29

Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
First fraction:
%28x%5E3%2B125%29%2F%28x%5E3-125%29
simplify using formula a^3+b^3=(a+b)(a^2-ab+b^2) and a^3-b^3=(a-b)(a^2+ab+b^2)
x^3+125=x^3+5^3= (x+5)(x^2-5x+25)
similary do with (x^3-125)
then:
%28%28x%2B5%29%28x%5E2-5x%2B25%29%29%2F%28%28x-5%29%28x%5E2%2B5x%2B25%29%29
Now first fraction multiply by inverse of second and simplify
%28%28x%2B5%29%28x%5E2-5x%2B25%29%29%2F%28%28x-5%29%28x%5E2%2B5x%2B25%29%29* %28x-5%29%2F%28x%5E2-5x%2B25%29=%28x%2B5%29%2F%28x%5E2%2B5x%2B25%29
*** you can not simplify x^2-5x+25 because it doesnt have roots b^2-4ac<0