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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.

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How about this

expr = (Sqrt[2]*
     Kf*(Cos[Sqrt[2]*(B/Kf)^(1/4)*L] + 
       Cosh[Sqrt[2]*(B/Kf)^(1/4)*L]))/((B/Kf)^(3/4)*(Sin[
        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

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