Спростити вираз : (1-1/b-1+1/b+1)+1/b^2 - вопрос №28094081111112 от kamely98 13.01.2020 06:06

Question

Математика: Спростити вираз : (1-1/b-1+1/b+1)+1/b^2

kamely98 · Answer

1 - (1/B - 1) + (1/B +1) = [ ( B-1)*(B +1) - (B +1) + ( B - 1 ) ] / (B^2 - 1 ) =
= ( B^2 - 1 - B - 1 + B - 1 ) / ( B^2 - 1 ) = ( B^2 - 3 ) / ( B^2 - 1 )

[ (B^2 - 3 ) / ( B^2 - 1 ) ] + ( 1/B^2 ) = ( B^2 * ( B^2 - 3 ) + B^2 - 1 ) / ( B^2 * (B^2 - 1) =
= ( B^4 - 3B^2 + B^2 - 1 ) / ( B^4 - B^2 ) =
= ( B^4 - 2B^2 - 1 ) / ( B^4 - B^2 )