How does $left(1+frac{x}{j}right)^{-1}left(1+frac{1}{j}right)^x=1+frac{x(x-1)}{2j^2}+Oleft(frac{1}{j^3}right)$

How does $$left(1+frac{x}{j}right)^{-1}left(1+frac{1}{j}right)^x=1+frac{x(x-1)}{2j^2}+Oleft(frac{1}{j^3}right)$$
my attempt: It looks like maybe the taylor series of the numerator at 1 times the geometric of the denominator:

$(1-(frac{x}{j})+(frac{x}{j})^2dots)(1+(1+1/j)^x(ln(1+1/j))(x-1)$

which obviously isn’t the right way. or simply expand the numerator and the second term of the polynomial:
$(1-(frac{x}{j})+(frac{x}{j})^2dots)((1+1/j)((1+1/j)^{x-1})$
which doesn’t give the x-1 on the right.