Expert: Sherman D. - 10/11/2008

Question
the problem is find f(a+h)- f(a) / h
heres the thing she gave us to solve:
f(x)= 3 / (x^2 +1)

i know how to solve normal problems but this is the first one that involves a fraction so please help me understand this.


Answer
f(x) = 3/(x^2 + 1)

f(a + h) = 3/((a + h)^2 + 1)
f(a) = 3/(a^2 + 1)

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

((3/(a^2 + 2ah + h^2 + 1)) - (3/(a^2 + 1)))/h

Multiply the top by (a^2 + 1)(a^2 + 2ah + h^2 + 1)

((3(a^2 + 1) - 3(a^2 + 2ah + h^2 + 1))/((a^2 + 1)(a^2 + 2ah + h^2 + 1)))/h

((3a^2 + 1 - 3a^2 - 6ah - 3h^2 - 3)/(a^4 + 2a^3h + a^2h^2 + 2a^2 + 2ah + h^2 + 1)/h

(-6ah - 3h^2 - 2)/(a^4 + 2a^3h + a^2h^2 + 2a^2 + 2ah + h^2 + 1)/(h/1)

(-6ah - 3h^2 - 2)/(a^4 + 2a^3h + a^2h^2 + 2a^2 + 2ah + h^2 + 1) * 1/h

(-6ah - 3h^2 - 2)/(a^4h + 2a^3h^2 + a^2h^3 + 3a^2h + 2ah^2 + h^3 + h)

that's what i got.