Giải Bài tập 19 trang 41 sgk Toán 8 tập 1 Chân trời

a) $\frac{8y}{3x^{2}}\times \frac{9x^{2}}{4y^{2}}=\frac{8y\times 9x^{2}}{3x^{2}\times 4y^{2}}=\frac{72x^{2}y}{12x^{2}y^{2}}=\frac{6}{y}$

b) $\frac{3x+x^{2}}{x^{2}+x+1}\times \frac{3x^{3}-3}{x+3}=\frac{x(x+3)\times 3(x-1)(x^{2}+x+1)}{(x^{2}+x+1)\times (x+3)}=3x(x-1)$

c) $\frac{2x^{2}+4}{x-3}\times \frac{3x+1}{x-1}:\frac{x^{2}+2}{6-2x}=\frac{2(x^{2}+2)\times (3x+1)\times [-2(x-3)]}{(x-3)\times (x-1)\times (x^{2}+2)}=\frac{-4(3x+1)}{x-1}$

d) $\frac{2x^{2}}{3y^{3}}:(-\frac{4x^{3}}{21y^{2}})=-\frac{2x^{2}\times 21y^{2}}{3y^{3}\times 4x^{3}}=\frac{-42x^{2}y^{2}}{12x^{3}y^{3}}=\frac{-7}{2xy}$

e) $\frac{2x+10}{x^{3}-64}:\frac{(x+5)^{2}}{2x-8}=\frac{2(x+5)\times 2(x-4)}{(x-4)(x^{2}+4x+16)\times (x+5)^{2}}=\frac{4}{(x^{2}+4x+16)(x+5)}$

g) $\frac{1}{x+y}(\frac{x+y}{xy}-x-y)-\frac{1}{x^{2}}:\frac{y}{x}=\frac{1}{x+y}\times \frac{x+y+x^{2}y-xy^{2}}{xy}-\frac{x}{x^{2}y}=\frac{x(1-xy)+y(x-xy)}{(x+y)\times xy}-\frac{1}{xy}$

$=\frac{(x+y)(1-xy)}{(x+y)xy}-\frac{1}{xy}=\frac{1-xy}{xy}-\frac{1}{xy}=\frac{-xy}{xy}=-1$