I have an expression:

$\frac{\sqrt{2} \text{Kf} \left(\cos \left(\sqrt{2} L \sqrt[4]{\frac{B}{\text{Kf}}}\right)+\cosh \left(\sqrt{2} L \sqrt[4]{\frac{B}{\text{Kf}}}\right)\right)}{\left(\frac{B}{\text{Kf}}\right)^{3/4} \left(\sin \left(\sqrt{2} L \sqrt[4]{\frac{B}{\text{Kf}}}\right)+\sinh \left(\sqrt{2} L \sqrt[4]{\frac{B}{\text{Kf}}}\right)\right)}$

(Sqrt[2] Kf (cos(Sqrt[2] L Power[B/Kf, (4)^-1]) + 
   cosh(Sqrt[2] L Power[B/Kf, (4)^-1])))/((B/Kf)^(
 3/4) (sin(Sqrt[2] L Power[B/Kf, (4)^-1]) + 
   sinh(Sqrt[2] L Power[B/Kf, (4)^-1])))

Obviously there's a pattern: $x = \sqrt[4]{\frac{1}{4}\frac{B}{K_f}}$

x = (B/Kf)^(1/4)/Sqrt[2]

enter image description here

But substituting it with a rule doesn't work:

enter image description here

Well, there's a workaround:

enter image description here

but I hope for a more straightforward approach.


1 Answer 1


How about this

expr = (Sqrt[2]*
     Kf*(Cos[Sqrt[2]*(B/Kf)^(1/4)*L] + 
        Sqrt[2]*(B/Kf)^(1/4)*L] + Sinh[Sqrt[2]*(B/Kf)^(1/4)*L]));
Assuming[x > 0, Simplify[expr /. B -> x^4*Kf*4]]

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.