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

Bài 19 trang 29 SBT Toán 8 Tập 1: 

a) $\frac{4}{x+\text{}2}+\text{\hspace{0.17em}}\frac{2}{x-2}+\text{\hspace{0.17em}}\frac{5x-6}{4-x^2}$;

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

c) $\frac{1}{x^2+\text{\hspace{0.17em}}6x\text{}+\text{\hspace{0.17em}}9}+\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{6x-x^2-9}+\text{\hspace{0.17em}}\frac{x}{x^2-9}$;

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

e) $\frac{x}{x-2y}+\text{\hspace{0.17em}}\frac{x}{x+\text{}2y}+\text{\hspace{0.17em}}\frac{4xy}{4y^2-x^2}$.

Lời giải:

a)

$\frac{4}{x+\text{\hspace{0.17em}}2}+\text{\hspace{0.17em}}\frac{2}{x-2}+\text{\hspace{0.17em}}\frac{5x-6}{4-x^2}$

$=\frac{4}{x+\text{\hspace{0.17em}}2}+\text{\hspace{0.17em}}\frac{2}{x-2}-\text{\hspace{0.17em}\hspace{0.17em}}\frac{5x-6}{x^2-4}$

$=\frac{4(x-2)+\text{}2(x+\text{}2)-(5x-6)}{(x-2).(x+2)}$

$=\frac{4x-8+\text{}2x+\text{\hspace{0.17em}}4-5x+\text{\hspace{0.17em}\hspace{0.17em}}6}{(x-2).(x+\text{}2)}$

$=\frac{x+\text{\hspace{0.17em}\hspace{0.17em}}2}{(x-2).(x+\text{}2)}=\frac{1}{x-2}$

b) $\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\text{\hspace{0.17em}}\frac{3x-2}{2x-4x^2}$

$=\frac{1-3x}{2x}+\frac{3x-2}{2x-1}-\text{\hspace{0.17em}}\frac{3x-2}{4x^2-2x}$

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

$=\frac{(1-3x).(2x-1)+(3x-2).2x-(3x-2)}{2x(2x-1)}$

$=\frac{2x-1-\text{\hspace{0.17em}}6x^2+3x+\text{\hspace{0.17em}}6x^2-4x-3x+\text{\hspace{0.17em}}2}{2x(2x-1)}$

$=\frac{-2x+1}{2x(2x-1)}=\frac{-(2x-1)}{2x(2x-1)}=\frac{-1}{2x}$

c) $\frac{1}{x^2+\text{\hspace{0.17em}}6x\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}9}+\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{6x-x^2-9}+\text{\hspace{0.17em}}\frac{x}{x^2-9}$

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

e) $\frac{x}{x-2y}+\text{\hspace{0.17em}}\frac{x}{x+\text{}2y}+\text{\hspace{0.17em}}\frac{4xy}{4y^2-x^2}$