How do you find the rate of change of f(x)= 3/x+1 on the interval [x,x+h} ? Please help!!! Thank you!!

Question

Please help! I am so confused in my college algebra class and my professor goes way too fast! Looking for a friend! Thank you!!!

Answer 1

Just the numerator

f(x) = 3/x + 1

f(x+h) = 3/(x+h) + 1

 

f(x+h) - f(x) = 3/(x + h) + 1 - (3/x + 1)

f(x+h) - f(x) = 3/(x+h) + 1 - 3/x - 1

f(x+h) - f(x) = 3/(x+h) - 3/x

f(x+h) - f(x) = (3x - 3(x + h)) / x(x+h)

f(x+h) - f(x) = (3x - 3x - h) / x(x+h)

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

f(x+h) - f(x) = -h / (x² + hx)

Now adding the denominator that is h

f(x+h) - f(x) = -1 / (x² + hx)

So as h → 0

f(x+h) - f(x) = -1 / x²