SOLUTION: I have the rational expression (n-9)/8 × (24n-24)/(9n-9) that I need to solve. I am confused on how I would simplify the second part. Would it be (n-1)/(n-1) or.....? Please help!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have the rational expression (n-9)/8 × (24n-24)/(9n-9) that I need to solve. I am confused on how I would simplify the second part. Would it be (n-1)/(n-1) or.....? Please help!      Log On


   

Question 837454: I have the rational expression (n-9)/8 × (24n-24)/(9n-9) that I need to solve. I am confused on how I would simplify the second part. Would it be (n-1)/(n-1) or.....? Please help!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, (n-9)/8 * (24n-24)/(9n-9) is an expression. Expressions cannot be solved. But they can be simplified.

%28%28n-9%29%2F8%29+%2A+%28%2824n-24%29%2F%289n-9%29%29 is, at a very basic level, a fraction times a fraction. When you first learned about multiplying fractions, before variables got involved, you should have learned that:
  • Cancelling/reducing may be done before the multiplication; and
  • Cancelling/reducing done before the multiplication makes the multiplication simpler.
  • Cancelling/reducing done when multiplying can be done with one factors of one fraction's numerators and another fraction's denominators. (This is called cross-cancelling.
This is not only still true but the advantage of Cancelling/reducing first is much, much greater now with the variables in the fractions than it ever was with just numbers!

So we are going to factor each numerator and denominator:

Cancel as much as we can, including cross-cancelling:

leaving:
%28%281%2A%28n-9%29%29%2F1%29+%2A+%281%2F3%29
And last we multiply:
%28n-9%29%2F3