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Question: another simplification challenge

Question:another simplification challenge

nm 11238 Maple 2025
simplification
May 08 2025
0

Is there a trick to make Maple simplify 

to

I can't use the exp() trick given in earlier questions, since there is no exp here. Below are my attempts. Can someone find another smart trick to do this simplification? Should simplify() have simplified it as is with no assumptions or using tricks? This is all done in code, so solutions can not depend on "looking on screen" and deciding what to do for each step.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

restart;
> 

interface(rtablesize=30);

[10, 10]

> 

A:=-(sqrt(3)*sqrt(-2*C1 - 2*x) - 3)/(3*sqrt(-2*C1 - 2*x)*x);

-(1/3)*(3^(1/2)*(-2*C1-2*x)^(1/2)-3)/((-2*C1-2*x)^(1/2)*x)

> 

B:=-(1/(sqrt(3)*x)) + 1/(sqrt(2)*x*sqrt(-x - C1));

-(1/3)*3^(1/2)/x+(1/2)*2^(1/2)/(x*(-x-C1)^(1/2))

> 

simplify(A-B);

0

> 

MmaTranslator:-Mma:-LeafCount(A);
MmaTranslator:-Mma:-LeafCount(B);

29

26

> 

full_simplify:=proc(e::anything,assum::anything)
   local result::list;

   #add more methods as needed

   result:=[(simplify(e) assuming assum),
            (simplify(e,size=false) assuming assum),
            (simplify(e,size) assuming assum),
            (simplify(e,sqrt) assuming assum),
            (simplify(combine(e)) assuming assum),
            (simplify(combine(e),size) assuming assum),
            (radnormal(evala( combine(e) )) assuming assum),
            (simplify(evala( combine(e) )) assuming assum),
            (evala(radnormal( combine(e) )) assuming assum),
            (simplify(radnormal( combine(e) )) assuming assum),
            (evala(factor(e)) assuming assum),
            (simplify(e,ln) assuming assum),
            (simplify(e,power) assuming assum),
            (simplify(e,RootOf) assuming assum),
            (simplify(e,sqrt) assuming assum),
            (simplify(e,trig) assuming assum),
            (simplify(convert(e,trig)) assuming assum),
            (simplify(convert(e,exp)) assuming assum),
            (combine(e) assuming assum)
   ];   
   RETURN( result )

end proc:
> 

Vector(full_simplify(A,real))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (6) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (8) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (10) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x)})

> 

Vector(full_simplify(A,positive))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (6) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (8) = -(1/6)*sqrt(2*C1+2*x)*(sqrt(3)*sqrt(2*C1+2*x)+3*I)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (10) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x)})

 

 

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