Giải bài 15 trang 39

Đề bài

Thực hiện phép tính:

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

b) $\frac{x+y}{2x-y}:\frac{1}{x-y}$

c) $\frac{x^{3}y+x{y}^3}{x^{4}y}:\left(x^2+y^2\right)$

d) $\frac{x^3+8}{x^2-2x+1}:\frac{x^2+3x+2}{1-x^2}$

Lời giải chi tiết

a) $\frac{1}{x^2-x+1}:\frac{x+1}{x-1}=\frac{1}{x^2-x+1}.\frac{x-1}{x+1}=\frac{x-1}{x^3+1}$

b) $\frac{x+y}{2x-y}:\frac{1}{x-y}=\frac{x+y}{2x-y}.\frac{x-y}{1}=\frac{x^2-y^2}{2x-y}$

c) $\frac{x^{3}y+x{y}^3}{x^{4}y}:\left(x^2+y^2\right)=\frac{xy\left(x^2+y^2\right)}{x^{4}y}.\frac{1}{x^2+y^2}=\frac{1}{x^3}$

d) $\frac{x^3+8}{x^2-2x+1}:\frac{x^2+3x+2}{1-x^2}=\frac{\left(x+2\right)\left(x^2-2x+y^2\right)}{{\left(x-1\right)}^2}.\frac{-\left(x-1\right)\left(x+1\right)}{\left(x+2\right)\left(x+1\right)}=-\frac{x^2-2x+4}{x-1}$