help with simplifying rational-expression product

susan pearson

New member
Joined
Aug 16, 2006
Messages
9
Would someone be so kind to check my answer on this problem?

Code:
 2xy - x - 2y + 1     y^3 - 27
------------------ . ----------  =
   2y^2 - 7y + 3       1 - x^2
The answer I came up with was

Code:
 y^2 + 3y +9
-------------
    1 + x
As you can see, I'm struggling. Thank you for helping!
 

galactus

Super Moderator
Staff member
Joined
Sep 28, 2005
Messages
7,216
You look good, except for one tiny little oversight.

It should be:

\(\displaystyle \L\\\frac{-(y^{2}+3y+9)}{x+1}\)

The negative comes from factoring \(\displaystyle 1-x^{2}\)

\(\displaystyle 1-x^{2}=(1-x)(x+1)\) or \(\displaystyle {-}(x-1)(x+1)\)

I assume you factored the variuos components.

\(\displaystyle \L\\\frac{\sout{(x-1)}\sout{(2y-1)}}{\sout{(y-3)}\sout{(2y-1)}}\cdot\frac{\sout{(y-3)}(y^{2}+3y+9)}{-\sout{(x-1)}(x+1)}\)

See that little negative in the denominator of the right side at the x-1.
 
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