10 / ( Х - 12) + 12 / ( Х - 10) = 2
10 * ( X - 10) + 12 * ( X - 12) = 2 * ( X - 10 ) * ( X - 12 )
10X - 100 + 12X - 144 = 2 * ( X^2 - 12X - 10X + 120 )
22X - 244 = 2X^2 - 44X + 240
2X^2 - 66X + 484 = 0
2 * ( X^2 - 33X + 242) = 0
D = 1089 - 968 = 121 ; √ D = 11
X1 = ( 33 + 11) : 2 = 22
X2 = ( 33 - 11) : 2 = 11
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X - 12 ≠ 0 ; X ≠ 12
X - 10 ≠ 0 ; X ≠ 10
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Ответ 22 и 11