Bài tập file word mức độ nhận biết Bài tập cuối chương VI

Câu 1:

a) Ta có:  $(x-3)(2y-x)(x-2y)$

$=-(3-x)(2y-x)(x-2y)=(3-x)(x-2y)^{2}$

$\Rightarrow \frac{(x-3)(2y-x)}{(x-2y)^{2}}$

$=\frac{3-x}{x-2y}$

b) Ta có:

$(4-3x)(16-9x^{2})=(4-3x)\left [ 4^{2}-(3x)^{2} \right ]$

$=(4-3x)(4-3x)(4+3x)$

$=(4+3x)(4-3x)^{2}(4+3x)(9x^{2}-24x+16)$

$=(4+3x)(4-3x)^{2}$

$\Rightarrow \frac{4-3x}{4+3x}$

$=\frac{9x^{2}-24x+16}{16-9x^{2}}$

Câu 2:

a) $\frac{x-1}{2x}+\frac{2x+1}{3x}+\frac{1-5x}{6x}$

$=\frac{3(x-1)+2(2x+1)+1-5x}{6x}=\frac{2x}{6x}=\frac{1}{3}$

b) $\frac{1}{x-y}+\frac{2}{x+y}+\frac{3}{y^{2}-x^{2}}$

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

$=\frac{-x-y+2y-2x+3}{y^{2}-x^{2}}$

$=\frac{-3x+y+3}{y^{2}-x^{2}}$

Câu 3:

a) $\frac{8x}{15y^{3}}.\frac{4y^{2}}{x^{2}}=\frac{32}{15xy}$

b) $\frac{24y^{5}}{7x^{2}}.(-\frac{21x}{12y^{3}})=-\frac{6y^{2}}{x}$

c) $\frac{9x^{2}}{x+3}.\frac{9-x^{2}}{6x^{3}}=\frac{9-3x}{2x}$

Câu 4:

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

b) $\frac{x^{2}-1-(x^{2}-4)}{x+1}=\frac{3}{x+1}$

Câu 5:

a) $\frac{x^{2}-y^{2}}{6x^{2}y}:\frac{x+y}{3xy}=\frac{x^{2}-y^{2}}{6x^{2}y}.\frac{3xy}{x+y}=\frac{(x-y)}{2x}$

b) $\frac{5x-15}{4x+4}:\frac{x^{2}-9}{x^{2}+2x+1}$

$=\frac{5x-15}{4x+4}.\frac{x^{2}+2x+1}{x^{2}-9}=\frac{5(x-3)}{4(x+1)}.\frac{(x+1)^{2}}{(x-3)(x+3)}$

$=\frac{5(x+1)}{4(x+3)}$