Hãy làm các phép chia Bài 36 trang 34 SBT Toán 8 Tập 1

Giải SBT Toán 8 Bài 8: Phép chia các phân thức đại số

Bài 36 trang 34 SBT Toán 8 Tập 1: Hãy làm các phép chia sau:

a) $\frac{7x+2}{3x{y}^3}:\text{\hspace{0.17em}\hspace{0.17em}}\frac{14x+\text{\hspace{0.17em}}4}{x^{2}y}$;

b) $\frac{8xy}{3x-1}:\text{\hspace{0.17em}\hspace{0.17em}}\frac{12x{y}^3}{5-15x}$;

c) $\frac{27-x^3}{5x+5}:\frac{2x-6}{3x+3}$;

d) $(\text{}4x^2-16):\frac{3x+\text{\hspace{0.17em}}6}{7x-2}$;

e) $\frac{3x^3+\text{\hspace{0.17em}\hspace{0.17em}}3}{x-1}:\text{\hspace{0.17em}\hspace{0.17em}}(x^2-x+\text{\hspace{0.17em}}1)$.

Lời giải:

a) $\frac{7x+2}{3x{y}^3}:\text{\hspace{0.17em}\hspace{0.17em}}\frac{14x+\text{\hspace{0.17em}}4}{x^{2}y}$

$=\frac{7x+2}{3x{y}^3}.\text{\hspace{0.17em}}\frac{x^{2}y}{14x+4}=\frac{(7x+2)x^{2}y}{3x{y}^3.(14x+4)}$

$=\frac{(7x+2)x^{2}y}{3x{y}^3.2(7x+2)}=\frac{x}{6y^2}$

b) $\frac{8xy}{3x-1}:\text{\hspace{0.17em}\hspace{0.17em}}\frac{12x{y}^3}{5-15x}$

$=\frac{8xy}{3x-1}.\frac{5-15x}{12x{y}^3}=\frac{8xy(5-15x)}{(3x-1)12x{y}^3}$

$=\frac{8xy.5(1-3x)}{(3x-1).12x{y}^3}=\frac{-10}{3y^2}$

c) $\frac{27-x^3}{5x+5}:\frac{2x-6}{3x+3}$

$=\frac{27-x^3}{5x+5}.\frac{3x+3}{2x-6}$

$=\frac{(27-x^3)(3x+3)}{(5x+5)(2x-6)}$

$=\frac{(\text{}3-x).(9+3x+x^2).3(x+1)}{5(x+1).2(x-3)}$

$=\frac{-3(9+3x+x^2)}{10}$

d) $(\text{}4x^2-16):\frac{3x+\text{\hspace{0.17em}}6}{7x-2}$

$=(\text{}4x^2-16).\frac{7x-2}{3x+6}=\frac{(4x^2-16)(7x-2)}{3x+6}$

$=\frac{(2x+4)(2x-4)(7x-2)}{3(x+2)}$

$=\frac{2(x+\text{}2)2(x-2)(7x-2)}{3(x+2)}=\frac{4(x-2).(7x-2)}{3}$

e) $\frac{3x^3+\text{\hspace{0.17em}\hspace{0.17em}}3}{x-1}:\text{\hspace{0.17em}\hspace{0.17em}}(x^2-x+\text{\hspace{0.17em}}1)$

$=\frac{3x^3+\text{\hspace{0.17em}\hspace{0.17em}}3}{x-1}.\frac{1}{x-_{2}x+1}\text{\hspace{0.17em}}$

$\begin{array}{l}=\frac{3(x^3+\text{\hspace{0.17em}\hspace{0.17em}}1).1}{(x-1)(x^2-x+\text{}1)}=\frac{3(x+\text{\hspace{0.17em}\hspace{0.17em}}1).(x^2-x+1)}{(x-1)(x^2-x+\text{}1)}\\ =\frac{3(x+1)}{x-1}\end{array}$