To simplify rational expressions in addition and subtraction you must get a common denominator first and form equivalent fractions. Then you combine the numerators and simplify the answer.

example 1/a + 1/b needs the common denominator ab.

rewrite as b/ab + a/ab and combine numerators.

You get (b + a) /ab and that cannot be simplified further.

To simplify rational expressions given multiplication, you may reduce first and then multiply numerators and multiply denominators and simplify the answer.

example.. 3/(2a +6 ) times ( a+3)/ 5

you may reduce the a+3 and the 2a + 6 because 2a + 6 **is** 2(a + 3).

So 3/2 times 1/5 is 3/10.

The key is to know to get common denominators in + and - and to

only reduce whole factors in multiplication and division.