Giải bài 4 trang 19

Đề bài

Rút gọn các phân thức sau:

a) $\frac{6ab}{-4ac}$;

b) $\frac{-a^{4}b}{-2a^2{b}^3}$;

c) $\frac{5a\left(a-b\right)}{10b\left(b-a\right)}$;

d) $\frac{3a\left(1-a\right)}{9{\left(a-1\right)}^2}$.

Lời giải chi tiết

a) $\frac{6ab}{-4ac}=\frac{3.2a.b}{-2.2a.c}=\frac{-3b}{2c}$;

b) $\frac{-a^{4}b}{-2a^2{b}^3}=\frac{-a^2.a^{2}b}{-2.a^2.b.b^2}=\frac{a^2}{2b^2}$;

c) $\frac{5a\left(a-b\right)}{10b\left(b-a\right)}=\frac{5a\left(a-b\right)}{-5.2b\left(a-b\right)}=\frac{-a}{2b}$;

d) $\frac{3a\left(1-a\right)}{9{\left(a-1\right)}^2}=\frac{3a\left(1-a\right)}{9{\left(1-a\right)}^2}=\frac{3a\left(1-a\right)}{3^2\left(1-a\right)\left(1-a\right)}=\frac{a}{3\left(1-a\right)}$.