SOLUTION: Divide and, if possible, simplify. x^2 + 7x + 10/x + 5 divided by x^2 - 4/5x - 10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Divide and, if possible, simplify. x^2 + 7x + 10/x + 5 divided by x^2 - 4/5x - 10      Log On


   

Question 173199This question is from textbook Introductory Algebra
: Divide and, if possible, simplify.
x^2 + 7x + 10/x + 5 divided by x^2 - 4/5x - 10 This question is from textbook Introductory Algebra

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

%28%28x%5E2%2B7x%2B10%29%2F%28x%2B5%29%29%2F%28%28x%5E2-4%29%2F%285x-10%29%29 Start with the given expression.


%28%28x%5E2%2B7x%2B10%29%2F%28x%2B5%29%29%28%285x-10%29%2F%28x%5E2-4%29%29 Multiply the first fraction %28x%5E2%2B7x%2B10%29%2F%28x%2B5%29 by the reciprocal of the second fraction %28x%5E2-4%29%2F%285x-10%29.


%28%28%28x%2B5%29%28x%2B2%29%29%2F%28x%2B5%29%29%28%285x-10%29%2F%28x%5E2-4%29%29 Factor x%5E2%2B7x%2B10 to get %28x%2B5%29%28x%2B2%29.


%28%28%28x%2B5%29%28x%2B2%29%29%2F%28x%2B5%29%29%28%285%28x-2%29%29%2F%28x%5E2-4%29%29 Factor 5x-10 to get 5%28x-2%29.


Factor x%5E2-4 to get %28x-2%29%28x%2B2%29.


%285%28x%2B5%29%28x%2B2%29%28x-2%29%29%2F%28%28x%2B5%29%28x-2%29%28x%2B2%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


5 Simplify.


So %28%28x%5E2%2B7x%2B10%29%2F%28x%2B5%29%29%2F%28%28x%5E2-4%29%2F%285x-10%29%29 simplifies to 5.


In other words, %28%28x%5E2%2B7x%2B10%29%2F%28x%2B5%29%29%2F%28%28x%5E2-4%29%2F%285x-10%29%29=5 where x%3C%3E-5, x%3C%3E-2 or x%3C%3E2