SOLUTION: Simplify the complex fractions. (2+ 1/4a)/(2/a-a) = ? (n/12- 2/9)/(n/6) = ? (a-9/1)/(1-3/a)= ? (2/x+3/x)/(4/x) = ? (x/2+x/3)/(x/4) = ? (2+1/a)/(2/a-a) = ? (

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify the complex fractions. (2+ 1/4a)/(2/a-a) = ? (n/12- 2/9)/(n/6) = ? (a-9/1)/(1-3/a)= ? (2/x+3/x)/(4/x) = ? (x/2+x/3)/(x/4) = ? (2+1/a)/(2/a-a) = ? (      Log On


   

Question 203372: Simplify the complex fractions.

(2+ 1/4a)/(2/a-a) = ?
(n/12- 2/9)/(n/6) = ?
(a-9/1)/(1-3/a)= ?
(2/x+3/x)/(4/x) = ?
(x/2+x/3)/(x/4) = ?
(2+1/a)/(2/a-a) = ?
(a-9/a)/(1-3/a) = ?
Sorry I know That's a lot.
Thanks

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way to simplify complex fractions is to:
Multiply the numerator and denominator of the "big" fraction by the Lowest Common Denominator of all the "little" fractions which are in the "big" fraction.
%282%2B+1%2F%284a%29%29%2F%282%2Fa-a%29
The "little" fractions are 1%2F%284a%29 and 2%2Fa. The LCD of these two is: 4a. So we will multiply the numerator and denominator of the "big" fraction by 4a:
%28%282%2B+1%2F%284a%29%29%2F%282%2Fa-a%29%29%28%284a%29%2F%284a%29%29
Using the Distributive Property to multiply the two numerators and the two denominators:
%282%284a%29+%2B+%281%2F%284a%29%29%284a%29%29%2F%28%282%2Fa%29%284a%29-a%284a%29%29
Simplify:

%288a+%2B+1%29%2F%282%2A4+-+4a%5E2%29
%288a+%2B+1%29%2F%288+-+4a%5E2%29

Problem: %28n%2F12-+2%2F9%29%2F%28n%2F6%29
The LCD of the "little" fractions is 36. So we will multiply the numerator and denominator of the "big" fraction by 36:
%28%28n%2F12-+2%2F9%29%2F%28n%2F6%29%29%2836%2F36%29
%28%28n%2F12%2936+-+%282%2F9%29%2836%29%29%2F%28%28n%2F6%2936%29
%283n+-+8%29%2F%286n%29

Problem: %28x%2F2%2Bx%2F3%29%2F%28x%2F4%29
The LCD of the "little" fractions is: 12. So we will multiply the numerator and denominator of the "big" fraction by 12:
%28%28x%2F2%2Bx%2F3%29%2F%28x%2F4%29%29%2812%2F12%29
%28%28x%2F2%2912+%2B+%28x%2F3%2912%29%2F%28%28x%2F4%2912%29
%286x+%2B+4x%29%2F%283x%29
%2810x%29%2F%283x%29
10%2F3

Now that you've seen several examples, I'll leave the rest for you.