[tex]a)E(x)=\frac{x^2-x-6}{x-3}-\frac{x^2-6x+8}{x-4}\\
E(x)=\frac{x^2-3x+2x-6}{x-3}-\frac{x^2-2x-4x+8}{x-4}\\
E(x)=\frac{x(x-3)+2(x-3)}{x-3}-\frac{x(x-2)-4(x-2)}{x-4}\\
E(x)=\frac{(x-3)(x+2)}{x-3}-\frac{(x-2)(x-4)}{x-4}\\
E(x)=x+2-x+2\\
E(x)=4=2^2 \vee x\in R-\{3,4\}\\
b)a=2x(1-2x^2)+4x^2(x+1)+2(x+2)\\
a=2x-4x^3+4x^3+4x^2+2x+4\\
a=4x^2+4x+4\\
a=4(x^2+x+1)\\
a=4(x^2+x+\frac{1}{4}+\frac{3}{4})\\
a=4[(x+\frac{1}{2})^2+\frac{3}{4}]\\ a=4(x+\frac{1}{2})^2+3\\Deci\ a \geq 0[/tex]
