Question

I just really don't understand how to solve this:
g(u) = 3/(u-2), find and simplify [g(x+h) - g(x)]/h. the fraction is just throwing me off

Answer 1

ok so instead of u you plug in (u+h)
\[g(u+h) = \frac{3}{(u+h)-2}\]

Answer 2

g(x+h) = 3/(x+h-2)
g(x) = 3/(x-2)
so, g(x+h) - g(x) = -3h / (x+h-2)(x-2)
so, (g(x+h) - g(x))/h = -3/(x+h-2)(x-2)

Answer 3

yeah like that ^^
what they did was combine the fractions with common denominator being
(u+h-2)(u-2)

Answer 4

This is what the numerator would look like
3(u-2) - 3(u+h-2) = 3u-3u-6+6 -3h = -3h

Answer 5

Thanks so much! You guys helped a ton