I have the following optimization problem:
minimize $f(x)=\dfrac{a}{x} + \dfrac{b}{d-c x} + f$
s.t $x\leq k$
Where $a,b,c,d,f>0$
Here is my approach using Lagrange multiplier: $L=f(x)+\lambda (x-k)$
(1)$\dfrac{\partial{L}}{\partial{x}}=-\dfrac{a}{x^2}+\dfrac{bc}{(d-cx)^2} + \lambda=0$
(2)$\dfrac{\partial{L}}{\partial{\lambda}}=x-k=0$
(3)$\lambda=\dfrac{a}{k^2}-\dfrac{b}{(d-ck)^2}$
I am stuck here. Replacing (3) in (1) yields an equation with degree 4. Is there any easier way to solve this. Need help!