# Thread: Complex Fractions

1. ## Complex Fractions

Ok so I need desparate help with complex fractions. Specificly the LCD part.i know its probably simple and Im most likely skipping or missing out on some rules but I only need to know specific things to pass the placment test and I atleast want to be placed in the classes I need and not some basic math class that will do nothin but waste my time and money.

So can anyone help me? I found an awesome site called coolmath.com I love it and it helps but I'm just not quite grasping what I need to do to master complex fractions

2. Example of one of the questions I need help with is...

2/x3 + 1/x / x/x-1+ 3/x2-1

2 1
___ + ___
x3 x
_______________

x 3
___ + ____
x-1 x2-1

3. Originally Posted by grlneedstoluvmath
Example of one of the questions I need help with is...

2/x3 + 1/x / x/x-1+ 3/x2-1
$\displaystyle \frac{2}{x^3}+\frac{\frac{1}{x}}{\frac{x}{x-1}}+\frac{3}{x^2-1}$

I am not sure if u mean this ..

$\displaystyle =\frac{2}{x^3}+\frac{x-1}{x^2}+\frac{3}{x^2-1}$

$\displaystyle =\frac{2(x^2-1)+x(x^2-1)(x-1)+3x^3}{x^3(x^2-1)}$

Then simplify it .

4. Hello, grlneedstoluvmath!

$\displaystyle \frac{\dfrac{2}{x^3} + \dfrac{1}{x}}{\dfrac{x}{x-1} + \dfrac{3}{x^2-1}}$
The LCD of all the denominators is: $\displaystyle x^3(x-1)(x+1)$

Multiply top and bottom by the LCD:

. . $\displaystyle \frac{x^3(x-1)(x+1)\left[\dfrac{2}{x^3}+\dfrac{1}{x}\right]} {x^3(x-1)(x+1)\left[\dfrac{x}{x-1} + \dfrac{3}{(x-1)(x+1)}\right]}$

. . $\displaystyle = \;\frac{2(x-1)(x+1) + x^2(x-1)(x+1)}{x^4(x+1) + 3x^3} \;= \;\frac{2x^2-2+x^4-x^2}{x^5 +x^4+3x^3}$

. . $\displaystyle = \;\frac{x^4+x^2-2}{x^3(x^2+x+3)} \;=\;\frac{(x^2-1)(x^2+2)}{x^3(x^2+x+3)}$