SOLUTION: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational       Log On


   

Question 1804: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
a rational equation, like %28x%2B2%29%2F%28x-1%29+=+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...
%28%28x%2B2%29%2F%28x-1%29%29%2A%28x-1%29+=+5%28x-1%29
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