Giải bài 6.32 trang 24

Đề bài

Thực hiện phép tính:

$\begin{array}{c}a)\frac{4x-6}{5x^2-x}.\frac{25x^2-10x+1}{27-8x^3}\\ b)\frac{2x+10}{{\left(x-3\right)}^2}:\frac{{\left(x+5\right)}^3}{x^2-9}\end{array}$

Lời giải chi tiết

$\begin{array}{c}a)\frac{4x-6}{5x^2-x}.\frac{25x^2-10x+1}{27-8x^3}\\ =\frac{-2\left(3-2x\right)}{x\left(5x-1\right)}.\frac{{\left(5x-1\right)}^2}{\left(3-2x\right)\left(9+6x+4x^2\right)}\\ =\frac{-2\left(5x-1\right)}{x\left(9+6x+4x^2\right)}\\ b)\frac{2x+10}{{\left(x-3\right)}^2}:\frac{{\left(x+5\right)}^3}{x^2-9}\\ =\frac{2x+10}{{\left(x-3\right)}^2}.\frac{x^2-9}{{\left(x+5\right)}^3}\\ =\frac{2\left(x+5\right)\left(x-3\right)\left(x+3\right)}{{\left(x-3\right)}^2{\left(x+5\right)}^3}\\ =\frac{2\left(x+3\right)}{\left(x-3\right){\left(x+5\right)}^2}\end{array}$