Compare the fractions n / M and n-a / M-A (m, N, a, are all non-zero natural numbers)

Compare the fractions n / M and n-a / M-A (m, N, a, are all non-zero natural numbers)

n/m-(n-a)/(m-a)
=[n(m-a)-m(n-a)]/m(m-a)
=[mn-na-mn+ma]/m(m-a)
=a(m-n)/m(m-a)
When m > n; m > a; n / m > (n-a) / (M-A);
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