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

Question

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

Answer 1

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 ) 
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[ (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 )