Expert: Richard J. Raridon - 10/21/2009

Question
Hi?? Good day!!!
I'm Leih Marie a 1st year collage student. Please help me solving this problem?? my brain was already squeezed out on finding the answer...here is the prob. it's all about "SIMPLIFYING COMPLEX RATIONAL ALGEBRAIC EXPRESSION"
                                4     6x+9
                               --- - ------
                                x     1+x
                       -------------------
                                  6-x
                                ------ +6
                                 1-x^2
                        2     
                       --- + --------------
                        x            x
                                3+ -----
                                    1-x

I have read different books but still I could not understand, and still could not solve for the correct answer..I hope you could sir!Thank You very much.  

Answer
Do you consider that all one problem?
Let's look at it in parts
4/x -(6x+9)/(1+x) = [4(1+x) -x(6x+9)]/[x(1+x)] = (4-5x-6x^2)/(x+x^2)

(6-x)/(1-x^2) +6 = (6-x+6-6x^2)/(1-x^2) = (12-x-6x^2)/(1-x^2)

2/x + 1/[3 +x/(1-x)] = 2/x +1/[3(1-x)+x]/(1-x) = 2/x +(1-x)/(3-2x) = (6-3x-x^2)/(3x-2x^2)

Maybe you can figure it out from there.