Aim : How do we simplify complex fractions ?

Argh.. ugly math again :(
but lets get started :

lets say one of your teachers gave you this problem :



So when dealing with complex fractions we have to solve it with parts.

First Step : Re-state your problem into parts.

4+ 1
     x
   
Second Step : In order to add fractions we need a common denominator.

For Example:

4+ 1
1    x  =   the common denominator would be x.

When you find the common denominator,you have to multiply the common denominator to the fraction that does not have it.

For example:
4 * x     = 4x
1 * x     =  x

Then, combine them
like this :
4x+ 1
  x

Third Step : After  you have done one part of the expression you go on to the second part.
3+ 2
     x2

Do the same steps as before, find a common denominator and multiply it to the fraction that does not have it.

So...  x2 is the common denominator.
So....

3   * x2  = 3x2
1   * x2  = x2

Unit them :

3x2 +2
 x2

Fourth Step : combine the whole expression.


4x+ 1  (÷)   3x2 +2
  x                x2

Fifth Step :  If a Expression has a diving symbol always use KFC, to change it to a multiplication.

K : keep
F : flip
C : change the bottom to the top

 K          F        C


4x+ 1     (÷)     3x2 +2
  x                       x2


Therefore :




4x+ 1   *      x2
  x             3x2+2

Sixth Step: Foil ALL possible pieces.

4x+1 = 4x+1
x       =   x



    X2      = (x) (x)
3x2+2    =  3x2+2

so :

4x+ 1   *  (x)(x)
   x           3x2+2

Seventh Step : Cross out what is repeated.

4x+ 1   *  (x)(x)
   x           3x2+2


P.s multiply x to 4x+1
Eight Step : Combine it all together for a final answer.

4x2+x

3x2+2

 A Problem :

 Works Cited:
Example Problem:  http://www.purplemath.com/modules/compfrac.htm
A Problem : http://www.regentsprep.org/Regents/math/algtrig/ATV2/simpcomplex.htm