Some tricky algebra

The gravitational potential enegry for a mass m at a distance R+h from the centre of the earth (where R is the radius of the earth) is -GMm/(R+h) where G is Newton's gravitational constant and M is the mass of the earth. If h << R, show that this is approximately equal to a constant (independent of h) plus mgh, where g=GM/R^2.

[Hint: write R+h = R(1+h/r) and expand (1+h/R)^(-1) using the binomial theorem.]

>>1
Cant' be done. You're black.

The hint gave you the answer basically...

-GMm/(R+h) = -GMm/R(1+h/R) ~ (-GMm/R)(1-h/R) = GMmh/R² - GMm/R = gmh + constant = mgh + constant