Question 1804
a rational equation, like {{{(x+2)/(x-1) = 5}}} is an EQUATION...2 things are equal, hence the equal sign in the middle. Equations have some rules (not many, admittedly). One such rule is that WHATEVER YOU DO TO ONE SIDE, YOU MUST DO TO THE OTHER SIDE AS WELL.

so, how do we get rid of the x-1 denominator? We multiply the LEFTHAND side by that value. However, if we do this to the lefthand side, then we HAVE TO do the same to the RIGHTHAND side, as...

{{{((x+2)/(x-1))*(x-1) = 5(x-1)}}}

Now, the LEFTHAND side cancels (this is why we did it, remember), and we are left with that version on the RIGHTHAND side. Now, people just call this cross-multiplying, but you are not strictly doing that. If you understand what lies beneath your "quick" method, then you understand what algebra is all about.

Now, as for a simple fraction, well hopefully you can now answer yourself :-)


cheers
Jon