SOLUTION: Divide and, if possible, simplify. (5x-15)/x ÷ (x-3)/(x^3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Divide and, if possible, simplify. (5x-15)/x ÷ (x-3)/(x^3)      Log On


   

Question 283977: Divide and, if possible, simplify.
(5x-15)/x ÷ (x-3)/(x^3)
Answer by JenniferTutors(83) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem:
%285x-15%29%2F%28x%29divided by%28x-3%29%2F%28x%5E3%29
You cannot divide the two fractions, you have to multiply the reciprocal (flip) the 2nd equation :
%285x-15%29%2F%28x%29 multiplied by %28x%5E3%29%2F%28x-3%29
Now you can simplify these fractions, if you notice 5x-15 can be simplified by taking a 5 out of the equation, both terms are a factor of 5:
5x-15
5%28x-3%29
This step is like going backwards, if that's clear.
Now your problem looks like this:
5%28x-3%29%2F%28x%29multiplied by %28x%5E3%29%2F%28x-3%29
If you notice, you have two terms that exact, which you can cross out:
5%2Across%28x-3%29%2F%28x%29multiplied by %28x%5E3%29%2Fcross%28x-3%29
Next notice the x's, you can subtract one from the other:
5%2Fcross%28x%29multiplied by %28x%5E3%29%2F%281%29
x%5E3+-+x+=+x%5E2
After that step:
%285%2F1%29multiplied by %28x%5E2%29%2F1
5x%5E2