Hi fellow b-school aspirants, veterans and GMAT scholars

Ive just started my GMAT mission, and am currently reading MGMATs Foundations of Math. In the fractions chapter, there are several problems at the end. There is one problem that goes like this:

**Quote:**

Multiply or divide the following fractions. Fractions should be in their most simplified form

7/(n+3) * (n+1)/2

The OA is (7n+7)/(2n+6) , but why cant we simplify that expression further, by cancelling 7n by 2n, making it 5n, and cancelling 7 by 6, making it 1,and thus we have the answer 5n + 1?

I understand theres a flaw in my knowledge of concept, is the reason this cancelling operation is illegal because we're dealing with addition as opposed to multiplication, or is there some other explanation?