Bài 1:

a, \(\frac{1}{-16}-\frac{3}{45}=\frac{-1}{16}-\frac{1}{15}\)

\(=\frac{-15}{240}-\frac{16}{240}\)

\(=\frac{-31}{240}\)

b, \(=\frac{-10}{12}-\frac{-12}{12}\)

\(=\frac{2}{12}=\frac{1}{6}\)

c, \(=\frac{-30}{6}-\frac{1}{6}\)

\(=\frac{-31}{6}\)

Bài 2:

a, \(x=-\frac{1}{2}-\frac{3}{4}\)

\(x=-\frac{1}{4}\)

b,   \(\frac{1}{2}+x=-\frac{11}{2}\)

\(x=-\frac{11}{2}-\frac{1}{2}\)

\(x=-6\)

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\(\frac{x-5}{3}=\frac{6}{5}\)

\(x-5=\frac{6}{5}.3\)

\(x-5=\frac{18}{5}\)

\(x=\frac{18}{5}+5\)

\(\Rightarrow x=\frac{43}{5}\)

Vậy ...

\(\frac{1}{3}=\frac{2-x}{4}\)

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

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

\(\Rightarrow x=\frac{2}{3}\)

Vậy ...

x - 5 = 6 * 3 / 5 => x - 5 = 3.6 => x = 8.6

2 - x = 4 / 3 => x = 2 / 3

\(\frac{2}{3}x-\frac{3}{2}\left(x-\frac{1}{2}\right)=\frac{5}{12}\)

\(\Rightarrow\frac{2}{3}x-\frac{3}{2}x+\frac{3}{4}=\frac{5}{12}\)

\(\Rightarrow\frac{-5}{6}x=\frac{5}{12}-\frac{3}{4}=\frac{-1}{3}\)

\(\Rightarrow x=\frac{-1}{3}:\frac{-5}{6}=\frac{2}{5}\)

vậy x = \(\frac{2}{5}\)

= 2/3x - 3/2x - 3/2 × 1/2= 5/12

=> -5/6x - 3/4 = 5/12

=> -5/6x = 5/12 +3/4= 7/6

=>x=7/6 ÷ -5/6 =1/3

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b) \(\frac{4}{9}x-\frac{1}{2}=\frac{-5}{9}\)

\(\Rightarrow\frac{4}{9}x=\frac{-5}{9}+\frac{1}{2}\)

\(\Rightarrow\frac{4}{9}x=\frac{-1}{18}\)

\(\Rightarrow x=\frac{-1}{18}:\frac{4}{9}\)

\(\Rightarrow x=\frac{-1}{8}\)

\(\frac{1}{4}+\frac{1}{3}:\left(2x-1\right)=-5\)

\(\frac{1}{3}:\left(2x-1\right)=-5-\frac{1}{4}\)

\(\frac{1}{3}:\left(2x-1\right)=-\frac{20}{4}-\frac{1}{4}\)

\(\frac{1}{3}:\left(2x-1\right)=-\frac{21}{4}\)

\(\left(2x-1\right)=\frac{1}{3}:-\frac{21}{4}\)

\(\left(2x-1\right)=\frac{1}{3}.-\frac{4}{21}\)

\(\left(2x-1\right)=-\frac{4}{63}\)

2x= -4/63 + 1

2x = 59/63

x = 59/63 : 2

x = 59/126

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

1/3:(2.x-1)=-21/4

2.x-1=1/3:-21/4

2.x-1=-4/63

2.x=-4/63+1

2.x=\(3\frac{59}{63}\)

x=\(3\frac{59}{63}\):2

x=\(1\frac{61}{63}\)

a) \(\frac{x}{4}=\frac{21}{28}\Rightarrow\frac{x}{4}=\frac{3}{4}\Rightarrow x=3\)

Vậy x = 3

b) \(\frac{2x}{5}=\frac{-24}{10}\Rightarrow\frac{2x}{5}=\frac{-12}{5}\Rightarrow2x=-12\Rightarrow x=-6\)

Vậy x = -6

\(a)\frac{x}{4}=\frac{21}{28}\)

\(\Rightarrow x\cdot28=4\cdot21\)

\(\Rightarrow x\cdot28=84\)

\(\Rightarrow x=3\)

\(b)\frac{2x}{5}=\frac{-24}{10}\)

Rút gọn : \(\frac{2x}{5}=\frac{-12}{5}\)

\(\Rightarrow2x=-12\)

\(\Rightarrow x=(-12)\div2=-6\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}=\frac{2001}{2003}\)

\(\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}\right)=\frac{1}{2}\cdot\frac{2001}{2003}\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{4006}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)

\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}\)

\(\frac{1}{x+1}=\frac{1}{2003}\)

\(\Rightarrow x+1=2003\)

\(x=2002\)

Vậy x = 2002

Bài này lớp 6 thật à bạn. 

\(\frac{5}{x}=\frac{2y+1}{6}=x\left(2y+1\right)=5.6=30.\)vì y thuộc z nên 2y+1 thuộc z và x thuộc z mà x(2y+1)=30 nên x;2y+1 thuộc Ư(30)={-1;1;2;-2;3;-3;5;-5;6;-6;10;-10;15;-15;30;-30}.

Vì 2y+1 là số lẻ nên ta có bảng sau:

Vậy các cặp số nguyên (x;y) thỏa mãn đề bài là:......................................