Question

Упростите выражение:

$frac{(m - n + 1)^2 - (m - 1 + n)^2}{4m}cdot(n + 1)$

Answer 1

$frac{(m-n+1)^2-(m-1+n)^2}{4m}*(n+1)=\\frac{((m-n+1)-(m-1+n))((m-n+1)+(m-1+n))}{4m}*(n+1)=\\frac{(m-n+1-m+1-n)(m-n+1+m-1+n)}{4m}*(n+1)=\\ frac{(-2n+2)*2m}{4m}*(n+1)=\\frac{4m(1-n)}{4m}*(1+n)=(1-n)(1+n)=1^2-n^2=1-n^2$