Question

数学指数函数 (m1/2-n1/2)/(m1/2+n1/2)+(m1/2+n1/2)/(m1/2-n1/2)

Answer 1

(m^1/2-n^1/2)/(m^1/2+n^1/2)+(m^1/2+n^1/2)/(m^1/2-n^1/2)

= (m^1/2-n^1/2)*(m^1/2-n^1/2)/[(m^1/2+n^1/2) (m^1/2-n^1/2)]+ (m^1/2+n^1/2)*(m^1/2+n^1/2)/[(m^1/2+n^1/2) (m^1/2-n^1/2)]

= (m^1/2-n^1/2)^2/[(m^1/2)^2-(n^1/2)^2]+(m^1/2+n^1/2)^2/[(m^1/2)^2-(n^1/2)^2]

=(m+n-2*m^1/2*n^1/2)/(m-n)+(m+n+2*m^1/2*n^1/2)/(m-n)

=(m+n-2*m^1/2*n^1/2m+n+2*m^1/2*n^1/2)/(m-n)

=2(m+n)/(m-n)