The transformation of [M2 + (√ 2) N2] / [M1 + (√ 2) N1] forms a + √ 2B

The transformation of [M2 + (√ 2) N2] / [M1 + (√ 2) N1] forms a + √ 2B

[m2+(√2)n2]/[m1+(√2)n1]
=[m2+(√2)n2][m1-(√2)n1]/[m1+(√2)n1][m1-(√2)n1]
=(m1m2-m2n1√2+m1n2√2-2n1n2)/(m1^2-2n1^2)
=(m1m2-2n1n2+(m1n2-m2n1)√2)/(m1^2-2n1^2)
=(m1m2-2n1n2)/(m1^2-2n1^2) +√2(m1n2-m2n1)/(m1^2-2n1^2)
Where a = (m1m2-2n1n2) / (M1 ^ 2-2n1 ^ 2) B = (m1n2-m2n1) / (M1 ^ 2-2n1 ^ 2)