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how to solve rational expressions

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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.