Question

What is the simplified form of the quantity of x plus 5, all over 2 + the quantity of x plus 6, all over 2?

Answer 1

Given

$\dfrac{x+5}{2}+\dfrac{x+6}{2}$

Find

The simplified form

Solution

There are a couple of possibilities, depending on whether you insist on a common denominator.

$\dfrac{x+5}{2}+\dfrac{x+6}{2}=\dfrac{(x+5)+(x+6)}{2}\\\\=\dfrac{2x+11}{2}\qquad\text{one possible representation of the sum}\\\\=x+\dfrac{11}{2}\qquad\text{another representation of the sum}$