Simplify these math expressions?

Question

3. For each of the functions, f, given , below, find the gradient of the secant joining the points P(a, f(a)) & Q(a+h, f(a+h))

3a. f(x) = 3+x^2

I got (2a^2)/h + 2a + h. The book says the answer is 2a+h. How'd they arrive at that?

3b. f(x) = x^3 + x

I got 3a^2 + 2ah + h2 + 2a/h + 1. The book's answer is 3a^2 + 1 + 3ah + h^2. How'd they arrive at that?

How did the book come to these answers? I feel that I am close to solving them but I am missing something. Please help. Thanks.

Answer 1

(f(a + h) – f(a)) / h =

= ((3 + (a + h)²) – (3 + a²)) / h =

= ((3 + (a² + 2ah + h²) – (3 + a²)) / h =

= (3 + a² + 2ah + h² – 3 - a²) / h =

= (2ah + h²) / h =

= 2a + h

-

(f(a + h) – f(a)) / h =

= (((a + h)³ + (a + h)) – (a³ + a)) / h =  

= (((a³ + 3a²h + 3ah² + h³) + (a + h)) – (a³ + a)) / h =  

= (a³ + 3a²h + 3ah² + h³ + a + h – a³ - a) / h =  

= (3a²h + 3ah² + h³ + h) / h =  

= 3a² + 3ah + h² + 1  

-