Question

16.aduceti la forma cea mai simpla
b)$\frac{2x-1}{ x^{3} -1 } - \frac{x}{x-1} +1$

Answer 1

$b) \frac{2x-1}{x^3-1}-\frac{x}{x-1}+1= \frac{2x-1-x( x^{2}+x+1)+ x^{3}-1}{x^3-1}=\frac{2x-1- x^{3}- x^{2}-x+x^3-1}{x^3-1}= \\=\frac{-x^2-x-2}{x^3-1}$
Am folosit formula de calcul prescurtat:
$a^3-b^3=(a-b)(a^2+ab+b^2)$
$x^3-1^3=(x-1)(x^2+x+1)$