An algebraic fraction is a fraction whose numerator, denominator, or both contain algebra. The top is called the numerator and the bottom is called the denominator.

They follow the same rules as ordinary fractions, but you can only cancel common factors. You must not cancel part of a sum such as the $x$ in $x+4$.

That is why factorising comes first. Useful patterns are:

$$3x^2+9x=3x(x+3)$$ $$x^2+7x+10=(x+5)(x+2)$$ $$x^2-25=(x-5)(x+5)$$