Evaluate the derivative of f(x) at x=1. That will give you the slope m of the tangent line at x=1.
f'(x) = [-3x2(x + x2) - (4 - x3)(1 + 2x)] / (x + x2)2
m = f'(1) = ?
Evaluate f(1). That will give you the tangent point (1,f(1)). Then finish by writing the equation of the line in point slope form.
y - y1 = m(x - x1)
x1 = 1
y1 = f(1)
m = f'(1)
You have everything you need, just plug in the numbers and evaluate.