Giải Bài 2 trang 39

Đề bài

Thực hiện các phép chia phân thức sau:

a) $\frac{5x}{4y^3}:\left(-\frac{x^4}{20y}\right)$                 

b) $\frac{x^2-16}{x+4}:\frac{2x-8}{x}$                     

c) $\frac{2x+6}{x^3-8}:\frac{{\left(x+3\right)}^3}{2x-4}$  

Lời giải chi tiết

a) $\frac{5x}{4y^3}:\left(-\frac{x^4}{20y}\right)$

$=\frac{5x}{4y^3}\cdot \frac{-20y}{x^4}=\frac{-100xy}{4x^4{y}^3}=\frac{-25}{x^3{y}^2}$

b) $\frac{x^2-16}{x+4}:\frac{2x-8}{x}$

$=\frac{\left(x-4\right)\left(x+4\right)}{x+4}\cdot \frac{x}{2x-8}=\frac{\left(x-4\right)\left(x+4\right)}{x+4}\cdot \frac{x}{2\left(x-4\right)}=\frac{x}{2}$

c) $\frac{2x+6}{x^3-8}:\frac{{\left(x+3\right)}^3}{2x-4}$

$=\frac{2\left(x+3\right)}{\left(x-2\right)\left(x^2+2x+4\right)}\cdot \frac{2\left(x-2\right)}{{\left(x+3\right)}^3}=\frac{4}{{\left(x+3\right)}^2\left(x^2+2x+4\right)}$