How do I simplify this difference quotient

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

Please show me how to plug f(x) and f(x+h) into the difference quotient so it can be simplified.

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

(-1/(x+h) - 1/x) / h ======> now what?

you didnt write it correct

f(x) = -1/x

so if you do f(x+h) - f(x)

will be -1/(x+h) - (-1/x)

now this is a fraction so you just have to find a common fraction

easy way is to mutiply the other fraction by x/x or (x+h)/(x+h)

so -1/(x+h)*(x/x)= -x/(x(x+h))

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

this means the difference is

-x/(x*(x+h)) + (x+h)/(x*(x+h))

since the denominators are the same we can make them one fraction

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

thats how you simplify

if this is a limit problem you then divide by h

and then take the limit