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Question: A=B but Maple does not want to simplify arctanh(A)-arctanh(B) = 0. Why?

Question:A=B but Maple does not want to simplify arctanh(A)-arctanh(B) = 0. Why?

nm 9934 Maple 2019
simplify
August 29 2019
2

A=B  but not able to simplify arctanh(A)-arctanh(B)  to be zero.  Why? Is there a workaround? Using Maple 2019.1

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restart;
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A:=((y*sqrt(3) + 3)*sqrt(3))/(6*sqrt(y^2 + 1));
B:=(y + sqrt(3))/(2*sqrt(y^2 + 1));
simplify(A-B)

(1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2)

(1/2)*(y+3^(1/2))/(y^2+1)^(1/2)

0

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simplify(arctanh(A)-arctanh(B))

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

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simplify(arctanh(A)-arctanh(B),trig)

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

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simplify(arctanh(A)-arctanh(B)) assuming positive

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

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simplify(arctanh(A)-arctanh(B),trig) assuming positive

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

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plot(arctanh(A),y=-Pi..Pi)

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plot(arctanh(B),y=-Pi..Pi)

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Download will_not_simplify.mw

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