Докажите тождество (4a/a^a-1+a-1/a+1)*2a/a+1-a/a-1-a/a^2-1=a^2/a^2-1 - вопрос №7824092411121121221 от stacezoloto 03.01.2022 09:22

Question

Алгебра: Докажите тождество (4a/a^a-1+a-1/a+1)*2a/a+1-a/a-1-a/a^2-1=a^2/a^2-1

stacezoloto · Answer

1)4a/[(a-1)(a+1)+(a-1)/(a+1)=[4a+(a-1)²]/[(a-1)(a+1)]=
=(4a+a²-2a+1)/[(a-1)(a+1)]=(a²+2a+1)/[(a-1)(a+1)]=
=(a+1)²/[(a-1)(a+1)]=(a+1)/(a-1)
2)(a+1)/(a-1)*2a/(a+1)=2a/(a-1)
3)2a/(a-1)-a/(a-1)=a/(a-1)
4)a/(a-1)-a/[(a-1)(a+1)]=a(a+1-1)/(a²-1)=a²/(a²-1)