Question

Упростить выражение.

Answer 1

$(x-1)sqrt{(1-x)^2+4x} /(x^2+1+ sqrt{4x^2} )= =(x-1) sqrt{1-2x+x^2+4x} /$$(x^2+1+/2x/)=(x-1) sqrt{(1+2x+x^2)} /(x^2+1+/2x/)=$$(x-1) sqrt{(1+x)^2} /(x^2+1+/2x/)=[(x-1)*/1+x/]/(x^2+1+/2x/)$
1)x<-1
(x-1)*(-1-x)/(x²+1-2x)=-(x-1)(1+x)/(x-1)²=(1+x)/(1-x)
2)-1≤x≤0
(x-1)(1+x)/(x²+1-2x)=(x-1)(1+x)/(x-1)²=(1+x)/(x-1)
3)x>0
(x-1)(1+x)/(x²+1+2x)=(x-1)(1+x)/(1+x)²=(x-1)/(1+x)