Ta có:

\(2^2>1.2\) ; \(3^2>2.3\); ....; \(n^2>\left(n-1\right)n\)

\(\Rightarrow\dfrac{1}{2^2}< \dfrac{1}{1.2}\) ; \(\dfrac{1}{3^2}< \dfrac{1}{2.3}\);...; \(\dfrac{1}{n^2}< \dfrac{1}{\left(n-1\right)n}\)

\(\Rightarrow P< \dfrac{1}{1^2}+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{\left(n-1\right)n}\)

\(\Rightarrow P< \dfrac{1}{1^2}+\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n-1}-\dfrac{1}{n}\)

\(\Rightarrow P< 2-\dfrac{1}{n}< 2\) (đpcm)

Số bị chia là:

20.10 + 4 = 204

Phá ngoặc:

-12x +3 = 87

12x = - 84

x=-7

-2.(\(x\) + 6) + 5.(3 - 2\(x\)) = 87

 -2\(x\) - 12 + 15  - 10\(x\)   = 87

-(2\(x\) + 10\(x\)) + (15 - 12) = 87

 -12\(x\)          + 3             = 87

 3 - 87  = 12\(x\)

12\(x\)       = -84

    \(x\)       = -84 : 12

     \(x\)      = -7

Lời giải:
a.

$=\frac{3}{5}-\frac{7}{4}=\frac{12-35}{20}=\frac{-23}{20}$

b.

$=-(2+\frac{5}{8})=-\frac{21}{8}$

c.

$=-(\frac{1}{8}+\frac{5}{9})=-\frac{9+8.5}{8.9}=\frac{-49}{72}$
d.

$=\frac{6}{13}-\frac{14}{39}=\frac{18}{39}-\frac{14}{39}=\frac{4}{39}$

e.

$=\frac{-3}{4}+\frac{5}{7}=\frac{5}{7}-\frac{3}{4}$

$=\frac{20-21}{7.4}=\frac{-1}{28}$

Lời gải:
$A=2x+7-3=2x+4$

$B=3x-8-12=3x-20$

\(\left(-7x-11\right)⋮\left(2x+4\right)\)

\(\Rightarrow2\left(-7x-11\right)⋮\left(2x+4\right)\)

\(\Rightarrow\left(-7x-11\right)⋮\left(x+2\right)\)

\(\Rightarrow\left(-7x-14+3\right)⋮\left(x+2\right)\)

\(\Rightarrow-7\left(x+2\right)+3⋮\left(x+2\right)\)

\(\Rightarrow3⋮\left(x+2\right)\)

\(\Rightarrow x+2=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(\Rightarrow x=\left\{-5;-3;-1;1\right\}\)

Thử lại thấy đều thỏa mãn, vậy \(x=\left\{-5;-3;-1;1\right\}\)