What is the limit of (x+7)/(3x+5) as x approaches infinity?

We need to find the limit of the
following.

==> lim (x+7) / (3x+5) as x-->
inf.

We will divide both numerator and denominator by
x.

==> lim ( x+ 7)/x /
(3x+5)/x

Now we will
simplify.

==> lim ( 1+ 7/x) / (3 +
5/x)

Now we will substitute with x =
inf.

==> lim (1+ 7/x) / (3+ 5/x) as x--> inf 
= ( 1+ 7/inf ) / ( 3+ 5/inf)

But we know that a/ inf =
0

==> lim (x+7)/(3x+5) as x--> inf = (1+ 0)/
(3+ 0) = 1/3

Then the limit is
1/3.