Simplifying rational expressions

Factor; make sure to denote values of the variable that are invalid (not in the domain).

Trick when encountering \(\frac{\left(x+6\right)\left(x-6\right)}{\left(6-x\right)}\): use the negative binomial: \(\frac{\left(x+6\right)\left(x-6\right)\cdot-1\cdot-1}{\left(6-x\right)}=\frac{\left(x+6\right)\left(-x+6\right)\cdot-1}{\left(6-x\right)}=-1\left(x+6\right)\)

Essentially: \(\dfrac{a-b}{b-a}=-1\) and \(a-b=-\left(b-a\right)=-b+a\)

Try substituting say \(a=x^2\) and solving with \(\)\(a\) instead.

Try factoring things out until you get a difference of squares or other familiar format.

The least common multiple of two numbers is the one that has the prime factorizations of both numbers and no more. A similar thing can be done with factorized polynomials.

For rational equations that have different denominators, multiply both sides by the LCM.