Why does the SIMPLE function within the Symbolic Math Toolbox return an incorrect result?

When I run the following code:

syms B

num = ((1+B)/(1-B))^(1/2);

den = ((1-B)/(1+B))^(1/2);

F = num/den;

F = simple(F)

pretty(F)

I receive the wrong solution:

    1 + B

     ------

   -1 + B

The solution should be:

    1 + B

     ------

    1 - B

Answer 1

[MathWorks Support Team]

This is a bug in Symbolic Math Toolbox 2.1.3 (R13) that has been brought to the attention of our development staff so that it may be fixed in a future release of Symbolic Math Toolbox.

As a workaround, try using the EXPAND function before using the SIMPLE function:

syms B

num = ((1+B)/(1-B))^(1/2)

den = ((1-B)/(1+B))^(1/2)

F = simple(expand(num)/expand(den))

pretty(F)