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Question: Why square roots are not simplifying in a fraction?

Question:Why square roots are not simplifying in a fraction?

mskalsi 290 Maple 18
radical substitution simplification pdetools
March 04 2022
1

Please see the attached file; I'm attempting to do some calculations with the 'PDETools' package; notice the first term in equation (4), where sqrt(x2+y2) is not canceling in the fraction, despite using the 'simplify' command; why is this happening, and how can I achieve complete simplification?

Ques_Mapleprime.mw

> 

with(PDEtools):
> 

DepVars := [u(x, y, t), U(xi, eta)]; 1; alias(u = u(x, y, t))

[u(x, y, t), U(xi, eta)]

  

u

 (1)
> 

xi[1] := 1/2*(x^2+y^2); 1; xi[2] := t; 1; u := (h(t)+(x^2+y^2)*(1/2))*arccos(x/sqrt(x^2+y^2))/t+U(xi[1], xi[2])

(1/2)*x^2+(1/2)*y^2

  

t

  

(h(t)+(1/2)*x^2+(1/2)*y^2)*arccos(x/(x^2+y^2)^(1/2))/t+U((1/2)*x^2+(1/2)*y^2, t)

 (2)
> 

(diff(u, x))*(diff(u, y))

(x*arccos(x/(x^2+y^2)^(1/2))/t-(h(t)+(1/2)*x^2+(1/2)*y^2)*(1/(x^2+y^2)^(1/2)-x^2/(x^2+y^2)^(3/2))/((1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*x)*(y*arccos(x/(x^2+y^2)^(1/2))/t+(h(t)+(1/2)*x^2+(1/2)*y^2)*x*y/((x^2+y^2)^(3/2)*(1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*y)

 (3)
> 

collect(simplify(subs(1/2*(x^2+y^2) = xi, t = eta, (x*arccos(x/(x^2+y^2)^(1/2))/t-(h(t)+(1/2)*x^2+(1/2)*y^2)*(1/(x^2+y^2)^(1/2)-x^2/(x^2+y^2)^(3/2))/((1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*x)*(y*arccos(x/(x^2+y^2)^(1/2))/t+(h(t)+(1/2)*x^2+(1/2)*y^2)*x*y/((x^2+y^2)^(3/2)*(1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*y))), D, 'distributed')

(1/4)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^3+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x*y^2)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^2+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*y^2)*(D[1](U))(xi, eta)^2/(y*(x^2+y^2)^2*eta^2)+(1/4)*((2*arccos(x/(x^2+y^2)^(1/2))*x^3*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*x*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2-x^2*y^2-y^4-2*h(eta)*y^2)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^2+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*y^2)+(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^3+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x*y^2)*(2*arccos(x/(x^2+y^2)^(1/2))*x^2*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2+x^3+x*y^2+2*h(eta)*x))*(D[1](U))(xi, eta)/(y*(x^2+y^2)^2*eta^2)+(1/4)*(2*arccos(x/(x^2+y^2)^(1/2))*x^3*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*x*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2-x^2*y^2-y^4-2*h(eta)*y^2)*(2*arccos(x/(x^2+y^2)^(1/2))*x^2*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2+x^3+x*y^2+2*h(eta)*x)/(y*(x^2+y^2)^2*eta^2)

 (4)
> 

``

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