SOLUTION: multiplication and division of rational expression; [[q^3+4q^2-5q]/[q^2-2q+1]÷[q^2+q-2]/[q^4-8q]] * [q-4]/[q^2-2q+4]

Algebra ->  Rational-functions -> SOLUTION: multiplication and division of rational expression; [[q^3+4q^2-5q]/[q^2-2q+1]÷[q^2+q-2]/[q^4-8q]] * [q-4]/[q^2-2q+4]      Log On


   

Question 888902: multiplication and division of rational expression;
[[q^3+4q^2-5q]/[q^2-2q+1]÷[q^2+q-2]/[q^4-8q]] * [q-4]/[q^2-2q+4]
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29÷%28q%5E2%2Bq-2%29%2F%28q%5E4-8q%29*%28q-4%29%2F%28q%5E2-2q%2B4%29

First we need to remember that a rational expression divided by a rational expression is the same as a rational expression times the other expressions reciprocal. So:

%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29÷%28q%5E2%2Bq-2%29%2F%28q%5E4-8q%29*%28q-4%29%2F%28q%5E2-2q%2B4%29
=%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29*%28q%5E4-8q%29%2F%28q%5E2%2Bq-2%29*%28q-4%29%2F%28q%5E2-2q%2B4%29

Now we Factor all the parts of this expression to see if anything cancels out.
%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29*%28q%5E4-8q%29%2F%28q%5E2%2Bq-2%29*%28q-4%29%2F%28q%5E2-2q%2B4%29
=%28q%28q%5E2%2B4q-5%29%29%2F%28%28q-1%29%5E2%29*%28q%28q%5E3-8%29%29%2F%28%28q-2%29%28q%2B1%29%29*%28q-4%29%2F%28q%5E2-2q%2B4%29
=%28q%28%28q-1%29%28q%2B5%29%29%29%2F%28%28q-1%29%5E2%29*%28q%28q-2%29%28q%5E2%2B2q%2B4%29%29%2F%28%28q-2%29%28q%2B1%29%29*%28q-4%29%2F%28q%5E2-2q%2B4%29

Now we see that the %28q-1%29 terms in the first expression cancel out as well as the %28q-2%29 terms in the second expression. The %28q%5E2%2B2q%2B4%29 terms also cancel out so we are left with:

=%28q%28q%2B5%29%29%29%2F%28q-1%29*q%2F%28q%2B1%29%29*%28q-4%29%2F1