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M-n/m^2-n^2 + ?/(m-1)(m-n) = 2m/m^2-n^2

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To solve for the missing value, we need to first find a common denominator for the fractions on the left side of the equation. The common denominator is (m - n)(m + n)(m - 1). Thus, we can write:

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

Next, we can cross-multiply to eliminate the fractions:

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

Simplifying the right side of the equation:

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

= 2m(m^2 - n^2)(m - 1)

Expanding the left side of the equation:

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

Distributing the left side of the equation:

(m - n)(m^2 - n^2 + ?) = (m - n)(m + n)(m - 1)

Canceling out the common factor (m - n):

m^2 - n^2 + ? = (m + n)(m - 1)

Expanding the left side of the equation:

? = (m + n)(m - 1) - (m^2 - n^2)

Simplifying the right side of the equation:

? = m^2 - m + n^2 + n - m^2 + n^2

= 2n^2 - m + n

Therefore, the missing value is ? = 2n^2 - m + n.

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