Arturo O. answered • 04/15/20

Experienced Physics Teacher for Physics Tutoring

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) = [-3x^{2}(x + x^{2}) - (4 - x^{3})(1 + 2x)] / (x + x^{2})^{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 - y_{1} = m(x - x_{1})

x_{1} = 1

y_{1} = f(1)

m = f'(1)

You have everything you need, just plug in the numbers and evaluate.