Giải câu 3 trang 51 toán VNEN 8 tập 1.
Cách 1:
$\frac{x – 1}{x}$.(x$^{2}$ + x + 1 + $\frac{x^{3}}{x - 1}$)
= $\frac{x – 1}{x}$.($\frac{(x^{2} + x + 1)(x – 1)}{x – 1}$ + $\frac{x^{3}}{x – 1}$)
= $\frac{x – 1}{x}$.($\frac{x^{3} – 1}{x – 1}$ + $\frac{x^{3}}{x – 1}$)
= $\frac{x – 1}{x}$.$\frac{2x^{3} – 1}{x – 1}$
= $\frac{2x^{3} – 1}{x}$.
Cách 2:
$\frac{x – 1}{x}$.(x$^{2}$ + x + 1 + $\frac{x^{3}}{x - 1}$)
= $\frac{x – 1}{x}$.x$^{2}$ + $\frac{x – 1}{x}$.x + $\frac{x – 1}{x}$.1 + $\frac{x – 1}{x}$.$\frac{x^{3}}{x – 1}$
= x(x – 1) + x – 1 + $\frac{x – 1}{x}$ + x$^{2}$
= 2x^{2} – 1 + $\frac{x – 1}{x}$
= $\frac{(2x^{2} – 1).x}{x}$
= $\frac{2x^{3} – 1}{x}$.