let f(x) = x + 2/x. Rewrite (f(x + h) - f(x)) /h as a simgle reduced fraction.

Answer 1

Hey! Let us solve this problem of the difference quotient, also known as the fundamental theorem of calculus! We must find the f(x+h) term since we have f(x) already. Then,

f(x+h) = (x+h) + 2/(x+h). Now, we can plug everything into the difference quotient such that it algebraically simplifies to,

[(x+h) + 2/(x+h)] - [(x+(2/x)] h(2x²+xh-x²-2) 2x²-x²+xh-2 x²+xh-2

------------------------------------- = -------------------- = ------------------ = ------------

h xh(x+h) x(x+h) x(x+h)

Hope this helps!