How do you simplify the rational expression: #(x+2)/(4x8)(3x9)/(x+4)(2x21)/(x^2x6)#?
1 Answer
Explanation:
The idea is to factor out numbers is the firstdegree polynomial (if possible), and to factor the highestdegree, finding their roots (if possible). So, let's work separately on the three pieces:

First fraction:
Numerator:#x+2># nothing to do;
**Denominator:#4x8># can factor a#4# , obtaining#4(x2)# . 
Second fraction:
Numerator:#3x9># can factor a#3# , obtaining#3(x3)# ;
**Denominator:#x+4># nothing to do. 
First fraction:
Numerator:#2x21># nothing to do;
**Denominator:#x^2x6># its roots are#3# and#2# , so we can write it as#(x3)(x+2)# .
Writing back the whole expression with this changes gives