Fractions

Ok, given:

(a/b)<(c/d)

how does one prove:

(a/b)<((a+c)/(b+d))<(c/d)

for all values of a, b, c and d? How do you prove it algebraically; not by substituting values to see it the inequality holds?
I tried this:

ad<bc

and

abd+ad^2<abd+bcd<b^2c+bcd

Then what? Please help!