Giải bài 2.19 trang 50

Đề bài

Thực hiện các phép tính sau:

a)     $\frac{15a^2}{8bc}.\frac{4c}{5a{b}^2}$

b)    $\frac{14x^3}{5y{z}^3}:\frac{7x}{15y{z}^2}$

c)     $\frac{6t+12}{10-5t}.\frac{t-2}{t+2}$

d)    $\frac{m-5}{m^2+1}:\left(3m-15\right)$

Lời giải chi tiết

a)     $\frac{15a^2}{8bc}.\frac{4c}{5a{b}^2}=\frac{15a^2.4c}{8bc.5a{b}^2}=\frac{3a.1}{2b.b^2}=\frac{3a}{2b^3}$

b)    $\frac{14x^3}{5y{z}^3}:\frac{7x}{15y{z}^2}=\frac{14x^3}{5y{z}^3}.\frac{15y{z}^2}{7x}=\frac{14x^3.15y{z}^2}{5y{z}^3.7x}=\frac{2x^2.3}{z}=\frac{6x^2}{z}$

c)     $\frac{6t+12}{10-5t}.\frac{t-2}{t+2}=\frac{\left(6t+12\right).\left(t-2\right)}{\left(10-5t\right).\left(t+2\right)}=\frac{6\left(t+2\right).\left(t-2\right)}{5\left(2-t\right)\left(t+2\right)}=\frac{6}{-5}$

d)    $\frac{m-5}{m^2+1}:\left(3m-15\right)=\frac{m-5}{m^2+1}.\frac{1}{3m-15}=\frac{\left(m-5\right)}{\left(m^2+1\right).3\left(m-5\right)}=\frac{1}{3\left(m^2+1\right)}$