linear algebra – How can I legally let terms go to 0 when taking the limit of a complex algebraic expression?

I have the following expression for one eigenvalue of a dynamical system:

$$lambda = -dfrac{1}{2} left ( (b+e+a+f+d+c) + sqrt{(b+e+a+f+d+c)^2 – 4(be+fb+bc+ae+ad+fd+ed+ac+fc)}right )$$.

I want to take the limit of this eigenvalue as a specific rate (e.g. b) goes to infinity. Is it legal to simplify the expression as follows?

$$lim_{b toinfty} lambda = -dfrac{1}{2} left ( b + sqrt{b^2 – 4cdot(3b)}right ) = -dfrac{1}{2} left ( b + sqrt{b^2 – 12b)}right )$$