Giải câu 3 Trang 43 sách VNEN toán 8 tập 1.

a) $\frac{x-1}{x^{3}+1}$ ; $\frac{2x}{x^{2}-x+1}$; $\frac{2}{x+1}$

Ta có: $\frac{x-1}{x^{3}+1}=\frac{x-1}{(x+1)(x^{2}-x+1)}$

MTC là $(x+1)(x^{2}-x+1)$

Suy ra: $\frac{x-1}{x^{3}+1}=\frac{x-1}{(x+1)(x^{2}-x+1)}$

$\frac{2x}{x^{2}-x+1}=\frac{2x(x+1)}{(x+1)(x^{2}-x+1)}$

$\frac{2}{x+1}=\frac{2(x^{2}-x+1)}{(x+1)(x^{2}-x+1)}$

b) $\frac{x+y}{x(y-z)^{2}}$; $\frac{y}{x^{2}(y-z)^{2}}$;  $\frac{z}{x^{2}}$

Ta có: MTC là $x^{2}(y-z)^{2}$

Suy ra: $\frac{x+y}{x(y-z)^{2}}=\frac{(x+y)x}{x^{2}(y-z)^{2}}$

$\frac{y}{x^{2}(y-z)^{2}}$

$\frac{z}{x^{2}}=\frac{z(y-z)^{2}}{x^{2}(y-z)^{2}}$