I need help with this: find (f(x+h)-f(x))/ h for this function..

Find (f(x-h)-f(x))/h for the function f(x)=x/(x+1)

So far, I got [((x+h)/(x+h+1)) - (x/(x+1))] /h

I'm stuck from there.

Any help would be appreciated.

You are doing good so far. At this point, clear the denominators in the numerator by multiplying the numerator and the denominator of the whole fraction by (x + 1)(x + h + 1). This gives:
[(x + h)/(x + h + 1) - x/(x + 1)]/h
= [(x + h)(x + 1) - x(x + h + 1)]/[h(x + 1)(x + h + 1)]
= [(x^2 + x + xh + h) - (x^2 + xh + x)]/[h(x + 1)(x + h + 1)], by expanding
= h/[h(x + 1)(x + h + 1)], by simplifying
= 1/[(x + 1)(x + h + 1)], by canceling h.

I hope this helps!

f(x) = x / (x+1)
f(x+h) = x+h / x + h + 1
f(x+h) - f(x) = x + h / x + h + 1 - x / x + 1
= [(x+h)(x+1) - (x+h+1)x] / (x+1)(x+h+1)
= x^2 + x + hx + h - x^2 - hx - x / (x+1)(x+h+1)
= h / (x+1)(x+h+1)
So f(x+h) - f(x) / h = 1 / (x+1)(x+h+1)

f(x h)-fx/h

its nothing but slope dy/dx at some point.

y=x/x 1

differentiating both sides we get,

dy/dx=1/(x 1) x/(x 1)^2

thats the answer(by shortcut)