Simplify an equation in Matlab (MuPAD)

Question

I have the following equation and want to simplify it using Matlab's MuPAD.

So, I used this in MuPAD:

Simplify(Gb = Gm*((2*(Gd+t)+3*Gm+3*P*(Gd+t-Gm))/(2*(Gd+t)+3*Gm-2*P*(Gd+t-Gm)))) 

and I get this:

Gb*(3*Gm + 2*Gd + 2*t - 2*P*(Gd - Gm + t)) = Gm*(3*Gm + 2*Gd + 2*t + 3*P*(Gd - Gm + t)) and 3*Gm + 2*Gd + 2*t <> 2*P*(Gd - Gm + t)

I cannot understand the first and second part (after "and"), what are these?

Answer 1

As per MuPAD's documentation, the relational operator <> denotes inequality, i.e., the left- and right-hand side are not equal. In other words, the simplification (before "and") is only valid if 3*Gm + 2*Gd + 2*t is not equal to 2*P*(Gd - Gm + t). This is the same thing as requiring that the denominator of the original expression not be zero (which would make it undefined).

Note that in MuPAD for Matlab R2015b, the <> operator is displayed as ≠ and "and" is rendered as ∧ (logical and):