Question

x+1/x-1+4/x^2-1+1-x/x+1
2x+1/x-2+1-2x/x+2+x^2+16/x^2-4
Multumesc

Answer 1

1) (x+1)/(x-1)+4/(x^2-1)+(1-x)/(x+1)=

=(x+1)/(x-1)+4/[(x-1)(x+1)]+(1-x)/(x+1)=

=[ numitorul comun este (x-1)(x+1) ]=

=[(x+1)^2 +4-(x-1)^2]/(x-1)(x+1)=

=(x^2 +2x+1+4-x^2 +2x-1)/(x-1)(x+1)=

(4x+4)/(x-1)(x+1)=4(x+1)/(x-1)(x+1)=4/(x-1)

2) (2x+1)/(x-2)+(1-2x)/(x+2)+(x^2+16)/(x^2-4)=

=(2x+1)/(x-2)+(1-2x)/(x+2)+(x^2+16)/[(x-2)(x+2)]=

=[numitorul comun este (x-2)(x+2) ]=

[(2x+1)(x+2)+(1-2x)(x-2)+x^2 +16]/[(x-2)(x+2)]=

=(2x^2 +4x+x+2+x-2-2x^2+4x+x^2 +16)/(x-2)(x+2)=

=(x^2 +10x +16)/(x-2)(x+2)=

=(x+2)(x+8)/(x-2)(x+2)=(x+8)/(x-2)