Please show work I am struggling with this problem thank you

Please show work, I am struggling with this problem, thank you.

Find and simplify the difference quotient f(x + h) - f(x)/h, h not equal to for the given function. f(x) = x^2 + 8 + 1 2x + h + 8 2x^2 + 2x + 2xh + h^2 + h + 2/h 1 2x + h + 1

Solution

f(x) = x^2 + 8x + 1

f(x+h) = (x + h)^2 + 8(x + h) + 1

= x^2 + h^2 + 2xh + 8x+ 8h + 1

(f(x + h) - f(x))/h = [x^2 + h^2 + 2xh + 8x+ 8h + 1 - (x^2 + 8x + 1)]/h

= (h^2 + 2xh + 8h)/h

= h + 2x + 8

(f(x + h) - f(x))/h = 2x + h + 8