Giải bài 6.9 trang 12

Đề bài

Rút gọn các phân thức sau:

a) $\frac{5x+10}{25x^2+50}$

b) $\frac{45x\left(3-x\right)}{15x{\left(x-3\right)}^3}$

c) $\frac{{\left(x^2-1\right)}^2}{\left(x+1\right)\left(x^3+1\right)}$

Lời giải chi tiết

a) $\frac{5x+10}{25x^2+50}$ $=\frac{5\left(x+2\right)}{25\left(x^2+2\right)}$ $=\frac{x+2}{5\left(x^2+2\right)}$

b) $\frac{45x\left(3-x\right)}{15x{\left(x-3\right)}^3}$ $=\frac{3\left(3-x\right)}{{\left(x-3\right)}^3}$ $=\frac{-3(x-3)}{(x-3{)}^3}$ $=\frac{-3}{(x-3{)}^2}$

c) $\frac{{\left(x^2-1\right)}^2}{\left(x+1\right)\left(x^3+1\right)}$

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

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

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