Its pretty simple:

X - (X²)/(X+h) acctually means:

(X²+hX-X²) / (X+h) which means:

hX / (X+h)

Now:

Lim (hX / (X+h)) when X-->infinite gives h/1 which is h.

Because the exponents of the X is equal in both the numerator and denominator.

Then you just have to calculate now how much is the coefficient of the X in the numerator devided by the coefficient of the X in the denominator.

This gives you h/1 which is h.

Hope this helps.