if f(x)=1divided by x+2, find and simplify f(a+h)-f(a)divided by h (h cannote equal zero)?

Question

Im bad at calculus and need help!

Answer 1

f(a)=1/(a+2)
f(a+h)= 1/(a+h+2)
f(a+h)-f(a)= 1/(a+h+2) - 1/(a+2)

Place terms over a common denominator of (a+2)*(a+h+2) to get
[(a+2)-(a+h+2)]/[(a+2)*(a+h+2)]

Simplify the numerator a+2-a-h-2 = -h

so f(a+h)-f(a) = -h/[(a+2)*(a+h+2)]

and [f(a+h)-f(a)]/h = -1/[(a+2)*(a+h+2)]

Answer 2

Substitute 'a + h' for the x, then substitute 'a' for x, all over 'h'.

1/ (a + h + 2) - 1 / (a + 2) divided by h
Finding common denominators,
(a + 2)/(a + h + 2)(a + 2) - (a + h + 2) / (a + h + 2)(a + 2)
all divided by h
Simplify: (a + 2 - a - h - 2) / h (a + 2) ( a + h + 2)
-h / h (a + 2) ( a + h + 2)
-1 / (a + 2)(a + h + 2)