1. ## Simplifying help.

Can someone show me how to simplify this.

$\displaystyle 6x\ln(1-xy)-\frac{3x^2y}{1-xy}+\frac{3x^2-2x^3y^2}{(1-xy)^2}$

I have had a few goes but I can't remember how to make them the same denominator. and keep coming up with a mash of rubbish , your help is appreciated.

2. For a start, note that in the term on the RHS you've got a factor of $\displaystyle 1-xy$ in the top and the bottom, so you can cancel that out of top and bottom to make it yay simpler. That means the 2nd and 3rd terms *do* have a common denominator. That should help for a start.

3. so
$\displaystyle \frac{3x^2-2x^2y}{1-xy}$??

4. Actually, now I look at it I may be wrong! I don't think that there is such a common factor after all.

So, take your initial equation and multiply top and bottom of the middle term by 1-xy to put it over a common denominator. Then it's a matter of sorting out the stuff on top and seeing whether there's a factor.