(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-2/3-m3/2)/(m+m^-1+1)

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(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-2/3-m3/2)/(m+m^-1+1)
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(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-2/3-m3/2)/(m+m^-1+1)
(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-2/3-m3/2)/(m+m^-1+1)

(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-2/3-m3/2)/(m+m^-1+1)
(m+m^-1+2)/(m^-1/2+m^1/2)*(m^-3/2-m^3/2)/(m+m^-1+1)
=(m^1/2+m^-1/2)^2/(m^-1/2+m^1/2)*(m^-1/2-m^1/2)*(m+m^-1+1)/(m+m^-1+1)
=(m^1/2+m^-1/2)*(m^-1/2-m^1/2)
=m^-1-m
=1/m-m