help with simplifying rational-expression product

[susan pearson]

Would someone be so kind to check my answer on this problem?

 2xy - x - 2y + 1     y^3 - 27
------------------ . ----------  =
   2y^2 - 7y + 3       1 - x^2

The answer I came up with was

 y^2 + 3y +9
-------------
    1 + x

As you can see, I'm struggling. Thank you for helping!

 

[galactus]

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.