Lấy máy tính tính đi, câu này dễ mà còn hỏi cho bằng được nữa =="

\(a,\dfrac{7}{35},\dfrac{18}{54},\dfrac{-15}{125},\dfrac{-4}{25}\)

Các thừa số đã tối giản : \(\dfrac{-4}{25}\)

\(\dfrac{7}{35}=\dfrac{7:7}{35:7}=\dfrac{1}{5}\) , \(\dfrac{18}{54}=\dfrac{18:18}{54:18}=\dfrac{1}{3}\)

\(\dfrac{-15}{125}=\dfrac{-15:5}{125:5}=\dfrac{-3}{25}\)

\(b,\dfrac{27}{45},\dfrac{21}{28},\dfrac{8}{14},\dfrac{18}{-60},\dfrac{-270}{360}\)

Các thừa số đã tối giản là : ko có

\(\dfrac{27}{45}=\dfrac{27:9}{45:9}=\dfrac{3}{5}\) , \(\dfrac{21}{28}=\dfrac{21:7}{28:7}=\dfrac{3}{4}\)

\(\dfrac{8}{14}\)\(=\dfrac{8:2}{14:2}=\dfrac{4}{7}\) , \(\dfrac{18}{-60}=\dfrac{18:6}{-60:6}=\dfrac{3}{-10}=\dfrac{-3}{10}\)

\(\dfrac{-270}{360}=\dfrac{-270:90}{360:90}=\dfrac{-3}{4}\)

\(c,\dfrac{3.4+3.7}{6.5+9}\) = \(\dfrac{3.\left(4+7\right)}{30+9}\) = \(\dfrac{3.11}{39}\) = \(\dfrac{3.11}{3.13}=\dfrac{11}{13}\)

\(\dfrac{-63}{81},\dfrac{9.6}{9.35},\dfrac{7.2+8}{2.14.5}\)

Các p/s đã tối giản : ko có

\(\dfrac{-63}{81}=\dfrac{-63:9}{81:9}=\dfrac{-7}{9}\) , \(\dfrac{9.6}{9.35}=\dfrac{6}{35}\)

\(\dfrac{7.2+8}{2.14.5}=\dfrac{14+8}{28.5}=\dfrac{22}{140}=\dfrac{11}{70}\)

Bài 2.

A = -3/5 + ( -2/5 + 2 )

A = -3/5 + ( -2/5 + 10/5 )

A = -3/5 + 8/5

A = 5/5

A = 1

--------------------------------------------------------

B = 3/7 + ( -1/5 + -3/7 )

B = 3/7 + ( -7/35 + -15/35 )

B = 3/7 + ( -22/35 )

B = 15/35 + ( -22/35 )

B = -1/5

-----------------------------------------------------

C = ( -5/24 + 0,75 + 7/12 ) : ( -2 . 1/8 )

C = ( -5/24 + 3/4 + 7/12 ) : ( -1/4 )

C = 9/8 : ( -1/4 )

C = 9/8 . ( -4 )

C = -9/2

Bài 3 .

a) 4/7 - x = 1/2 . x + 2/7

<=> -x - x = 1/2 - 4/7 + 2/7

<=> -2x = 3/14

<=> x = 3/14 . ( -1/2 )

<=> x = -3/28

Vậy x = -3/28

b) x : 3 1/5 = 1 1/2

<=> x : 16/5 = 3/2

<=> x = 3/2 . 16/5

<=> x = 24/5

Vậy x = 24/5

c) x . 3/4 = -1 5/8

<=> x . 3/4 = -13/8

<=> x = -13/8 . 4/3

<=> x = -13/6

Vậy x = -13/6

Bài 4.

a) ( 2 1/3 + 3 1/2 ) . x = -4 1/6 + 3 1/7

<=> ( 7/3 + 7/2 ) . x = -25/6 + 22/7

<=> 35/6 . x = -43/42

<=> x = -43/42 . 6/35

<=> x = -43/245

Vậy x = -43/245

b) x : ( 3 1/2 - 5 1/6 ) = 4 1/5 - 6 2/3

<=> x : ( 7/2 - 31/6 ) = 21/5 - 20/3

<=> x : ( 21/6 - 31/6 ) = -37/15

<=> x : ( -5/3 ) = -37/15

<=> x = -37/15 . ( -5/3 )

<=> x = 37/9

Vậy x = 37/9

\(\dfrac{8-2x}{x^2+x-20}=-\dfrac{2\left(4-x\right)}{\left(4-x\right)\left(x+5\right)}=\dfrac{-2}{x+5}\)

Để biểu thức trên nhận giá trị dương khi 

\(x+5< 0\)do -2 < 0 

\(\Leftrightarrow x< -5\)

Đề lỗi không?

a: ĐKXĐ:\(x\notin\left\{2;0\right\}\)

b: \(C=\left(\dfrac{x\left(2-x\right)}{2\left(x^2+4\right)}-\dfrac{2x^2}{\left(x-2\right)\left(x^2+4\right)}\right)\cdot\left(\dfrac{2-x^2+x}{x^2}\right)\)

\(=\dfrac{-x^3+4x^2-4x-4x^2}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{x\left(x^2+4\right)}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{\left(x-2\right)\left(x+1\right)}{x^2}=\dfrac{x+1}{2x}\)

c: Thay x=2017 vào C, ta được:

\(C=\dfrac{2017+1}{2\cdot2017}=\dfrac{1009}{2017}\)

\(\left(\dfrac{\dfrac{x}{x+1}}{\dfrac{x^2}{x^2+x+1}}-\dfrac{2x+1}{x^2+x}\right)\dfrac{x^2-1}{x-1}\)ĐK : \(x\ne\pm1\)

\(=\left(\dfrac{x}{x+1}.\dfrac{x^2+x+1}{x^2}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)=\left(\dfrac{x^2+x-1}{x^2+x}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)\)

\(=\left(\dfrac{x^2+x-1-2x-1}{x\left(x+1\right)}\right)\left(x+1\right)=\dfrac{x^2-3x-2}{x}\)

à xin lỗi mình nhầm dòng cuối 

\(=\dfrac{x^2-x-2}{x}=\dfrac{\left(x+1\right)\left(x-2\right)}{x}\)

Để biểu thức trên nhận giá trị dương khi 

\(\dfrac{\left(x+1\right)\left(x-2\right)}{x}>0\)bạn tự xét TH cả tử và mẫu nhé, mình đánh trên này bị lỗi 

a) \(A=\sqrt{18}.\sqrt{2}-\sqrt{48}:\sqrt{3}=\sqrt{18.2}-\sqrt{48:3}\)

\(=\sqrt{36}-\sqrt{16}=6-4=2\)

b) \(B=\dfrac{8}{\sqrt{5}-1}+\dfrac{8}{\sqrt{5}+1}=\dfrac{8\sqrt{5}+8+8\sqrt{5}-8}{\left(\sqrt{5}-1\right).\left(\sqrt{5}+1\right)}=\dfrac{16\sqrt{5}}{4}=4\sqrt{5}\)