How can factoring and LCMs help make solving rational equations simpler? Provide an example.

Factoring and using least common multiples can help in solving rational equations by seeing what is in the numerator and denominator and find the common parts. If we do not have the same parts that can be cancelled, we can try grouping or expanding either the denominator or the numerator and find the part that can be cancelled after.

An example of this is:

x^2+10x+25/x+5

at first sight it does not look like it has any parts to be cancelled, but when we factor the numerator we get:

(x+5)(x+5)/(x+5)

Here we see that we can take out part of the numerator and all the denominator and we be left with:

x+5