\(-\frac{3}{x}=\frac{x}{-27}\)

\(\Leftrightarrow x.x=-3.\left(-27\right)\)

\(x^2=81\)

\(x=\pm9\)

Ta có :\(\frac{-3}{x}=\frac{x}{-27}\)
=> x . x = -3(-27)
=> x^2= 81 
=> x^2 = (±9)^2
=> x =±9
Vậy ....
Hok tốt...:))

\(a,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{97.98}+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{100}{100}-\frac{1}{100}\)

\(=\frac{99}{100}\)

\(b,\frac{x}{y}=\frac{3}{5}\)

\(\Leftrightarrow\frac{x}{3}=\frac{y}{5}\)

\(\text{Áp dụng tính chất dãy tỉ số bằng nhau ta có :}\)

\(\frac{x}{3}=\frac{y}{5}=\frac{x+y}{3+5}=\frac{18}{8}=\frac{9}{4}\)

\(\Rightarrow\frac{x}{3}=\frac{9}{4}\Rightarrow x=\frac{27}{4}\)

\(\frac{y}{5}=\frac{9}{4}\Rightarrow y=\frac{45}{4}\)

....................../????????????

Đề sai ạ 

Đề real ( theo đề ôn hsg chỗ mk )

A= \(\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\)\(\frac{4n-5}{n-3}\)

A = \(\frac{2n+1+3n-5-4n-5}{n-3}\)

A = \(\frac{n-9}{n-3}\)

Để A mang giá trị nguyên thì n- 9 \(⋮\)n-3

=> n-3 - 6 \(⋮\)n - 3 

=> -6 \(⋮\)n-3

=> n-3 \(\in\)Ư(-6) = { -6 ; -3 ; -2 ; -1 ; 1 ; 2 ; 3 ; 6 }

=> n - 3 \(\in\){ -6 ; -3 ; -2 ; -1 ; 1 ; 2 ; 3 ; 6 }

=> n \(\in\){ -3 ; 0 ; 1 ; 2 ; 4 ; 5 ; 6 ; 9 }

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

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

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

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

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

\(4a+19\text{ là bội của }a+3\)

\(\Leftrightarrow4a+19⋮a+3\)

\(a+3⋮a+3\)

\(\Rightarrow4\left(a+3\right)⋮a+3\)

\(4a+12⋮a+3\)

\(\Rightarrow\left(4a+19\right)-\left(4a+12\right)⋮a+3\)

\(4a+19-4a+12⋮a+3\)

\(31⋮a+3\)

\(\Rightarrow a+3\in\text{Ư}\left(31\right)=\left\{\pm1;\pm31\right\}\)

Ta có bảng : .....................

Tự làm típ nhó !

4a + 19 là bội số của a + 3

\(\Rightarrow4a+19⋮a+3\)

\(4a+12+7⋮a+3\)

\(4\left(a+3\right)+7⋮a+3\)

\(\Rightarrow\hept{\begin{cases}4\left(a+3\right)⋮a+3\\7⋮a+3\end{cases}}\)

\(7⋮a+3\)

\(\Rightarrow a+3\in\)Ư (7) = {-7;-1;1;7}

\(\Rightarrow a\in\left\{-11;-4;-2;4\right\}\)

Mk k nhìn rõ đầu bài, có j sai thì thông cảm nhe 

\(\left(-1\right)^{200}-\left(x-2\right)^5=33^1\)

\(1-\left(x-2\right)^5=33\)

\(\left(x-2\right)^5=33+1\)

\(\left(x-2\right)^5=34\)

\(x^5-2^5=34\)

\(x^5-32=34\)

\(x^5=34+32\)

\(x^5=66\)

\(x=\sqrt[5]{66}\)

MK làm luôn nhé

=2.(1/3+1/5+1/9)

5.(1/3+1/7+1/9)

=2/5

20,21x52,74+202,1x4,736-2,021

=2,021x10x52,74+2,021x100x4,736-2,021

=2,021x527,4+2,021x473,6-2,021

=2,021x(527,4+473,6-1)

=2,021x1000

=2021