Question

how is adding and subtracting rational expressions similar to adding and subtracting simple fraction ?

Answer 1

In both cases you make the denominator common and then add or subtract the numerator.

To add fractions 1/2 and 1/3, the common denominator is 6
1/2 = (1*3) / (2*3) = 3/6
1/3 = (1*2) / (3*2) = 2/6
Add
1/2 + 1/3 = 3/6 + 2/6 = (3+2) / 6 = 5/6

You do the same with rational expressions.
Add: 1/x + 1/(x + 1).
Common denominator is x(x+1)
1/x + 1/(x + 1) = (x+1) / {x(x+1)} + x / {x(x+1)}
= (x+1+x) / {x(x+1)}
= (2x+1)/{x(x+1)}