this is where m = 2

|x|--n--|x|--n--|x|

taking care of the lengths of fence you have m * n.
now you have to take care of the posts. The posts are always between each length of fence as well as at the beginning and after. As the picture shows, that is always 1 more than the number of fence pieces. You can see in the picture, 3 posts for 2 fence pieces.

(m+1)x thus gives you the total length of the posts.

m * n + (m+1)x

then factor

m*n + mx + x
m(n + x) + x

One way to think about counting the number of posts correctly:

Think of the posts as being attached to every length of fence on the left side of the length.

So it goes: PL-PL-PL....
equal number of posts and lengths ...
until the very end, when we will need 1 post on the right to close it off:
...PL-PL-PL-P

That means the number of posts is equal to the number of lengths, plus 1.