SOLUTION: Find each product x^-25 x+5 ------ * ------- 9 x-5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find each product x^-25 x+5 ------ * ------- 9 x-5      Log On


   

Question 189074This question is from textbook
: Find each product
x^-25 x+5
------ * -------
9 x-5 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-25%29%2F%289%29%29%28%28x%2B5%29%2F%28x-5%29%29 Start with the given expression.


%28%28%28x-5%29%28x%2B5%29%29%2F%289%29%29%28%28x%2B5%29%2F%28x-5%29%29 Factor x%5E2-25 to get %28x-5%29%28x%2B5%29 (use the difference of squares).


%28%28x-5%29%28x%2B5%29%28x%2B5%29%29%2F%289%28x-5%29%29 Combine the fractions.


%28highlight%28%28x-5%29%29%28x%2B5%29%28x%2B5%29%29%2F%289%2Ahighlight%28%28x-5%29%29%29 Highlight the common terms.


%28cross%28%28x-5%29%29%28x%2B5%29%28x%2B5%29%29%2F%289%2Across%28%28x-5%29%29%29 Cancel out the common terms.


%28%28x%2B5%29%28x%2B5%29%29%2F%289%29 Simplify.


%28x%5E2%2B10x%2B25%29%2F%289%29 FOIL


So %28%28x%5E2-25%29%2F%289%29%29%28%28x%2B5%29%2F%28x-5%29%29 simplifies to %28x%5E2%2B10x%2B25%29%2F%289%29.


In other words, %28%28x%5E2-25%29%2F%289%29%29%28%28x%2B5%29%2F%28x-5%29%29=%28x%5E2%2B10x%2B25%29%2F%289%29 where x%3C%3E5