I have been trying to solve this problem for the past two days please help

Question

find difference quotient f(a+h)-f(a)/ h....

Question 1)

f(a) = a/a+3

f(a+h)= a+h/a+h+3

f(a+h)-f(a) /h=????

Answer 1

f(a) = a / (a + 3)

f(a+h) = (a + h) / (a + h + 3)

[f(a+h) - f(a)] / h = [((a + h) / (a + h + 3)) - (a / (a + 3))] / h

= [((a + h)(a + 3) - a(a + h + 3)) / ((a + h + 3)(a + 3))] / h

= [((a² + 3a + ah + 3h) - (a² + ah + 3a)) / (a² + ah + 3a + 3a + 3h + 9)] / h

= [3h / (a² + ah + 6a + 3h + 9)] / h

= 3 / (a² + ah + 6a + 3h + 9)

Answer 2

(a+h)/(a+h+3) - a/(a+3)

the common denominator is (a+h+3)(a+3)

[(a+h)(a+3) - a(a+h+3)]/[ (a+h+3)(a+3)] =

[ a^2 + ah + 3a + 3h - a^2 - ah - 3a]/ [ (a+h+3)(a+3)]=

a^2 cancels, ah cancels, 3a cancels

3h / [ (a+h+3)(a+3)]

Finally divides by h:

3 / [ (a+h+3)(a+3)]=