SOLUTION: dividing 2x/x-4 (divide) 8/x2-7x+12) (note that x2 is x squared.) the fact that they are not all ax-bx+c is throwing me off. Not sure how to move forward

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: dividing 2x/x-4 (divide) 8/x2-7x+12) (note that x2 is x squared.) the fact that they are not all ax-bx+c is throwing me off. Not sure how to move forward      Log On


   

Question 370727: dividing
2x/x-4 (divide) 8/x2-7x+12)
(note that x2 is x squared.)
the fact that they are not all ax-bx+c is throwing me off.
Not sure how to move forward
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%29%2F%28x-4%29%29%2F%288%2F%28x%5E2-7x%2B12%29%29
As usual when dividing fractions, you change it to multiplying the reciprocal:
%28%282x%29%2F%28x-4%29%29%2A%28%28x%5E2-7x%2B12%29%2F8%29
When you first learned to multiply fractions you probably learned that common factors in the numerators and denominators can be canceled, even across from one fraction to another. You also probably learned that doing so made the multiplication easier. This is all still true. In fact the advantage of canceling before multiplying is even greater now than it was long ago.

In order to cancel factors we need to know what the factors are. So we start by factoring the numerators and denominators:
%28%282%2Ax%29%2F%281%2A%28x-4%29%29%29%2A%28%28%28x-4%29%28x-3%29%29%2F%282%2A4%29%29
Now we should be able to that several factors can be canceled:

which leaves:
%28x%2F1%29%2A%28%28x-3%29%2F4%29
This is much easier to multiply that what we had before!
%28x%2A%28x-3%29%29%2F%281%2A4%29
which simplifies to:
%28x%5E2-3x%29%2F4