Question

f(x)=x/x+1 for (f(x+h)-f(x))/h

Answer 1

\[\frac{\frac{x+h}{x+h+1}-\frac{x}{x+1}}{h}\]

Answer 2

\[\frac{\frac{(x+h)(x+1)-x(x+h+1)}{(x+h+1)(x+1)}}{h}\]

Answer 3

\[\frac{\frac{x^2+x+hx+h-x^2-hx-x}{(x+h+1)(x+1)}}{h}\]

Answer 4

\[\frac{h}{(x+h+1)(x+1)}\times\frac{1}{h}=\frac{1}{(x+h+1)(x+1)}\]

Answer 5

Are you supposed to find the limit as h approaches 0?

Answer 6

no just the difference quotient

Answer 7

this is the answer but I didnt understand how to do the problem thank you for explaining how you go to the answer.

Answer 8

got*