SOLUTION: I have the problem: 1 1 __ - __ 4n 2 *OVER* n 1 __- ___ 6 24n and I need to simplify. I solved the problems for the numerator and denominator and got: -4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have the problem: 1 1 __ - __ 4n 2 *OVER* n 1 __- ___ 6 24n and I need to simplify. I solved the problems for the numerator and denominator and got: -4      Log On


   

Question 203076: I have the problem:
1 1
__ - __
4n 2
*OVER*
n 1
__- ___
6 24n
and I need to simplify. I solved the problems for the numerator and denominator and got:
-4n+2 144n
_____ x _____
6n 24n^2-6 .....using the reciprocal of the denominator to multiply by.
from there, I got that 24n^2-6 factors to (-4n+2)(-6n-3) and so that can cross cancel with the -4n+2 in the first fraction. the 144n can cross cancel with the 6n. So, I got:
1 24
__ x ____
1 -6n-3 From here, I can factor out a -3, which makes it: -8/2n+3, but that
is not one of the options. The options are: -6/2n-1, -6/2n+1, or 6/2n+1. What did I do wrong?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1 1
__ - __
4n 2
*OVER*
n 1
__- ___
6 24n
Assume the problem is:
%281%2F%284n%29%29+-+%281%2F2%29
------------
%28n%2F6%29-%281%2F%2824n%29%29
:
Common denominators
%281-2n%29%2F%284n%29
------
%284n%5E2-1%29%2F%2824n%29
invert the dividing fraction and multiply, cancel out 4n, factor the dif of squares
%281-2n%29%2F%284n%29 * %2824n%29%2F%284n%5E2-1%29 = (1-2n) * 6%2F%284n%5E2-1%29 = 6%281-2n%29%2F%284n%5E2-1%29 = 6%281-2n%29%2F%28%282n%2B1%29%282n-1%29%29
We can rewrite the numerator, then cancel 2n-1:
%28-6%282n-1%29%29%2F%28%282n%2B1%29%282n-1%29%29 = %28-6%29%2F%28%282n%2B1%29%29 or -6%2F%282n%2B1%29