Well...here is the original problem:

...and my aproach:

=

Now the lowest common factor would be and we rewrite the expression as:

=

Which is the same as:

=

And finally I have:

=

Now my questions is Can this expression be further simplified? As I see we could still make 4x and 2x compensate to obtain

=

=

but the book I'm working with states the solution is just

Could it be that simplification works when numerator and denominator imply multiplication only? Mmm...