Question

Алгебра 8 класс, помогите пж, дам 30 баллов

Answer 1

task/30341621   доказать тождество

(2x-2)/(4x²+4x+4) +3x/(2x³-2)+1/(2x-2) = (x-1)/(x²+x+1)    ???

решение (2x-2) /(4x²+4x+4) +3x/(2x³-2) +1/(2x-2) =

2(x-1)/4(x²+x+1) +3x/2(x³-1) +1/2(x-1) =

(x-1)/2(x²+x+1) +3x/2(x-1)(x²+x+1) +1/2(x-1) =

( (x-1)² +3x +(x²+x+1) ) / 2(x-1)(x²+x+1) =

(x²-2x+1 +3x +x²+x+1) / 2(x-1)(x²+x+1) =(2x²+2x+2) / 2(x-1)(x²+x+1) =

2(x²+x+1) / 2(x-1)(x²+x+1) = 1/(x-1) .