An algebraic fraction is just a fraction whose top and bottom are expressions in x rather than plain numbers. You simplify it the very same way you reduce a numeric fraction such as \frac{6}{9} = \frac{2}{3}: find a factor shared by the top and the bottom, and cancel it.

The trick with algebra is that the shared factor is usually hidden until you factorise the top and the bottom first. Take this fraction:

The numerator is a difference of two squares, so it factorises as (x + 3)(x - 3). Now an (x + 3) sits in both the top and the bottom — a common factor we can cancel:

That is the whole idea: factorise top and bottom, then cancel the common factor. What is left is the simplified fraction.

See it built

Watch the top get factorised, then the matching (x + 3) on the top and the bottom get crossed out, leaving x - 3. Step through it.

See it explained

Sal Khan factorises the top and bottom of rational expressions and cancels the shared factors to write them in lowest terms.