ЯсноПонятно24

Разложим дроби на простейшие:

(b/(b^2-8b+16) - (b+6)/(b^2-16)) / (b+12)/(b^2-16) = 2/(b-4)

b/(b-4)^2 - (b+6)/(b-4)(b+4) / (b+12)/(b-4)(b+4) = 2/(b-4)

b/(b-4)^2 - (b+6)/(b^2-16) / (b+12)/(b^2-16) = 2/(b-4)

b(b+12) - (b+6)(b-4) = 2(b^2-16)

b^2 + 12b - b^2 + 4b - 24 = 2b^2 - 32

16b - 24 = 2b^2 - 32

16b - 24 = 2(b^2 - 16)

16b - 24 = 2(b-4)(b+4)

16b - 24 = 2(b-4)

16b - 24 = 2b - 8

14b = 16

b = 8/7

Таким образом, доказано тождество (b/(b^2-8b+16)-(b+6)/(b^2-16))∶(b+12)/(b^2-16)=2/(b-4) для b = 8/7.