SOLUTION: For all values of the variables for which the expression is defined, perform the indicated operation and express the result in simplest form. {{{(r^2-7r+10)/(5r-r^2)}}}÷{{{(r^2-4)/

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For all values of the variables for which the expression is defined, perform the indicated operation and express the result in simplest form. {{{(r^2-7r+10)/(5r-r^2)}}}÷{{{(r^2-4)/      Log On


   

Question 1036640: For all values of the variables for which the expression is defined, perform the indicated operation and express the result in simplest form. %28r%5E2-7r%2B10%29%2F%285r-r%5E2%29÷%28r%5E2-4%29%2F%2825r%5E3%29
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For all values of the variables for which the expression is defined, perform the indicated operation and express the result in simplest form.
%28r%5E2-7r%2B10%29%2F%285r-r%5E2%29÷%28r%5E2-4%29%2F%2825r%5E3%29
invert the dividing fraction and multiply
%28r%5E2-7r%2B10%29%2F%285r-r%5E2%29*%2825r%5E3%29%2F%28r%5E2-4%29
Factor
%28%28r-2%29%28r-5%29%29%2F%28r%285-r%29%29*%2825r%5E3%29%2F%28%28r-2%29%28r%2B2%29%29
Factor out -1 so we can cancel the (r-5)
%28%28r-2%29%28r-5%29%29%2F%28-1r%28r-5%29%29*%2825r%5E3%29%2F%28%28r-2%29%28r%2B2%29%29
Cancel -r, (r-5), (r-2), you are left with
%28-25r%5E2%29%2F%28%28r%2B2%29%29