help with simplifying rational-expression product

susan pearson

New member
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
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.