Question

expresia.. va rog este urgent

Answer 1

E(x)=(7x-3x²)/(1-9x²) -3x/(1-2x-3x²) ×(1+ (3x+x²)/(x+3)=

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

=(7x-3x²)/(1-3x)(1+3x) -3x/(1+x)(1-3x) ×(x+3+ 3x+x²)/(x+3)=
=(7x-3x²)/(1-3x)(1+3x) -3x/(1+x)(1-3x) ×(x²+4x+3)/(x+3)=

x²+4x+3=x²+3x+x+3=x(x+3)+(x+3)=(x+3)(x+1)

=(7x-3x²)/(1-3x)(1+3x) -3x/(1+x)(1-3x) ×(x+3)(x+1)/(x+3)=
=(7x-3x²)/(1-3x)(1+3x) -3x/(1-3x)=
=(7x-3x²-3x-9x²)/(1-3x)(1+3x)=
=(4x-12x²)/(1-3x)(1+3x)=
=4x(1-3x)/(1-3x)(1+3x)=
=4x/(1+3x)