Let's simplify the expression step by step:
Given expression: (m+n)^2 - (m-n)(m+n) / m^2n + n^2m
First, expand the terms in the numerator:= (m^2 + 2mn + n^2) - (m^2 - mn + mn - n^2) / m^2n + n^2m= m^2 + 2mn + n^2 - m^2 + mn - mn + n^2 / m^2n + n^2m= 2mn + 2n^2 / m^2n + n^2m
Next, simplify the expression further:= 2n(m + n) / mn(m + nm)= 2n / n(m + n)= 2 / (m + n)
Therefore, the simplified form of the expression (m+n)^2 - (m-n)(m+n) / m^2n + n^2m is 2 / (m + n).
Let's simplify the expression step by step:
Given expression: (m+n)^2 - (m-n)(m+n) / m^2n + n^2m
First, expand the terms in the numerator:
= (m^2 + 2mn + n^2) - (m^2 - mn + mn - n^2) / m^2n + n^2m
= m^2 + 2mn + n^2 - m^2 + mn - mn + n^2 / m^2n + n^2m
= 2mn + 2n^2 / m^2n + n^2m
Next, simplify the expression further:
= 2n(m + n) / mn(m + nm)
= 2n / n(m + n)
= 2 / (m + n)
Therefore, the simplified form of the expression (m+n)^2 - (m-n)(m+n) / m^2n + n^2m is 2 / (m + n).