SOLUTION: x to the 5th power plus y to the 5th power divided by x plus y. Can you please help?

Algebra ->  Exponents -> SOLUTION: x to the 5th power plus y to the 5th power divided by x plus y. Can you please help?      Log On


   

Question 164452: x to the 5th power plus y to the 5th power divided by x plus y. Can you please help?
Found 2 solutions by jim_thompson5910, padmameesala:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E5%2By%5E5%29%2F%28x%2By%29 Start with the given expression


%28%28x%2By%29%28x%5E4-x%5E3y%2Bx%5E2y%5E2-xy%5E3%2By%5E4%29%29%2F%28x%2By%29 Factor the numerator


Highlight the common terms.


Cancel out the common terms


x%5E4-x%5E3y%2Bx%5E2y%5E2-xy%5E3%2By%5E4 Simplify


So %28x%5E5%2By%5E5%29%2F%28x%2By%29 simplifies to x%5E4-x%5E3y%2Bx%5E2y%5E2-xy%5E3%2By%5E4


In other words, %28x%5E5%2By%5E5%29%2F%28x%2By%29=x%5E4-x%5E3y%2Bx%5E2y%5E2-xy%5E3%2By%5E4 where x%3C%3E-y

Answer by padmameesala(42) About Me  (Show Source):
You can put this solution on YOUR website!

x4-x3y+x2y2-xy3+y4
--------------------------------------
x + y ) x5 + y5
x5+x4y (x+y)* x4
----------
-x4y
-x4y - x3y2 (x+y) *-x3y
--------------
x3y2
x3y2+ x2y3 (x+y) *x2y2
---------------
- x2y3
- x2y3- xy4 (x+y)*-xy3
-------------
xy4
xy4+ y5 (x+y) *y4
-----------
0
your answer is x4-x3y+x2y2-xy3+y4
Please note that all the numbers represent the powers
and all the steps product is written on the right side
Hope you will understand this problem
good luck