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Question: Re: Further simplification

Question:Re: Further simplification

pik1432 245 Maple 2020
radical simplification
December 08 2020
0

Hello there, 

Would you allow me to ask this question?

What would be a way to simplify the expression 'eq9_32a' below to the 'Desired' expression?

Intuitively, the numerator and denominator can be divided by 'sqrt(r^2 + 1)', but the 'Simplify' instruction did not do that. 
 

> 

restart;
> 

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

 (1)
> 

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

 (2)
> 

eq9_32a :=  T__e_np = simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

T__e_np = (r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (3)
> 

Desired := T__e_np = 1/(sqrt(r^2 + 1) + r);

T__e_np = 1/((r^2+1)^(1/2)+r)

 (4)
> 

 


Merry Christmas!

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