Solving Limits Algebreically

How do you solve the following limits algebrically?

Lim X----->0 (-1/(3+x)+1/3)/ (x)


Lim h----->0 ((x+h)^2+(x+h))-(X^2+x)/h

to solve algebraically, simplify the fractions first

1) [ -1/(3+x)+(1/3)]/x
in the numerator, get a common denominator

= [(-3+3+x)/3(3+x)] * 1/x

= (x)[(9+3x)(x)]

= 1/(9+3x)

Now lim (x->0)= 1/9

2) {[ (x+h)^2+(x+h)]-(x^2+x)}/ h. Is the whole difference over h?( it is actually the derivative)

= (x^2+2xh+h^2+x+h-x^2-x)/h

= (2xh+h^2+h)/h

= 2x+h+1

Lim(h->0)= 2x+1

Hoping this helps!