Cộng các phân thức cùng mẫu thức Bài 17 trang 28 SBT Toán 8 Tập 1

Giải SBT Toán 8 Bài 5: Phép cộng các phân thức đại số

Bài 17 trang 28 SBT Toán 8 Tập 1: 

a) $\frac{1-2x}{6x^{3}y}+\text{\hspace{0.17em}}\frac{3+\text{\hspace{0.17em}}2y}{6x^{3}y}+\text{\hspace{0.17em}}\frac{2x-4}{6x^{3}y}$;

b) $\frac{x^2-2}{x{(x-1)}^2}+\frac{2-x}{x{(x-1)}^2}$;

c) $\frac{3x+\text{\hspace{0.17em}}1}{x^2-3x+\text{\hspace{0.17em}}1}+\text{\hspace{0.17em}}\frac{x^2-6x}{x^2-3x+\text{\hspace{0.17em}}1}$;

d) $\frac{x^2+38x+\text{\hspace{0.17em}}4}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}+\text{\hspace{0.17em}}\frac{3x^2-4x-2}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}$ .

Lời giải:

a) 

$\begin{array}{l}\frac{1-2x}{6x^{3}y}+\text{\hspace{0.17em}}\frac{3+\text{\hspace{0.17em}}2y}{6x^{3}y}+\text{\hspace{0.17em}}\frac{2x-4}{6x^{3}y}\\ =\frac{1-2x+\text{}3+\text{}2y+\text{}2x-4}{6x^{3}y}=\frac{2y}{6x^{3}y}=\frac{1}{3x3}\end{array}$

b) 

$\begin{array}{l}\frac{x^2-2}{x{(x-1)}^2}+\frac{2-x}{x{(x-1)}^2}\\ =\frac{x^2-2+\text{}2-x}{x{(x-1)}^2}=\frac{x^2-x}{x{(x-1)}^2}\\ =\frac{x(x-1)}{x{(x-1)}^2}=\frac{1}{x-1}\end{array}$

c) 

$\begin{array}{l}\frac{3x+\text{\hspace{0.17em}}1}{x^2-3x+\text{\hspace{0.17em}}1}+\text{\hspace{0.17em}}\frac{x^2-6x}{x^2-3x+\text{\hspace{0.17em}}1}\\ =\frac{3x+\text{\hspace{0.17em}}1+\text{\hspace{0.17em}}{x}^2-6x}{x^2-3x+\text{\hspace{0.17em}}1}=\frac{x^2-3x+\text{\hspace{0.17em}}1}{x^2-3x+\text{\hspace{0.17em}}1}=1\end{array}$

d)

$\begin{array}{l}\frac{x^2+38x+\text{\hspace{0.17em}}4}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}+\text{\hspace{0.17em}}\frac{3x^2-4x-2}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}\\ =\text{\hspace{0.17em}}\frac{x^2+\text{\hspace{0.17em}}38x+\text{\hspace{0.17em}}4+\text{\hspace{0.17em}}3x^2-4x-2}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}\end{array}$

$=\frac{4x^2+34x+\text{\hspace{0.17em}}2}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}=\frac{2.\left(2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1\right)}{2x^2+\text{\hspace{0.17em}}17x+\text{\hspace{0.17em}}1}=2$