\(D=\dfrac{2\sqrt{x}+1}{\sqrt{x}-3}=\dfrac{2\left(\sqrt{x}-3\right)+7}{\sqrt{x}-3}=2+\dfrac{7}{\sqrt{x}-3}\left(x\ge0;x\ne9\right)\)

Để \(D\) nguyên thì \(2+\dfrac{7}{\sqrt{x}-3}\) nguyên

\(\Rightarrow \dfrac{7}{\sqrt x-3}\) nguyên

\(\Rightarrow7⋮\sqrt{x}-3\)

\(\Rightarrow\sqrt{x}-3\inƯ\left(7\right)\)

\(\Rightarrow\sqrt{x}-3\in\left\{1;7;-1;-7\right\}\)

\(\Rightarrow\sqrt{x}\in\left\{4;10;2;-3\right\}\) mà \(\sqrt{x}\ge0\)

\(\Rightarrow\sqrt{x}\in\left\{4;10;2\right\}\)

\(\Rightarrow x\in\left\{16;100;4\right\}\left(tm.đk.x.nguyên\right)\)

Kết hợp với điều kiện, ta được: \(x\in\left\{4;16;100\right\}\)

\(D=\dfrac{2\sqrt[]{x}+1}{\sqrt[]{x}-3}\in Z\left(x\ge0;x\ne9\right)\)

\(\Leftrightarrow2\sqrt[]{x}+1⋮\sqrt[]{x}-3\)

\(\Leftrightarrow2\sqrt[]{x}+1-2\left(\sqrt[]{x}-3\right)⋮\sqrt[]{x}-3\)

\(\Leftrightarrow2\sqrt[]{x}+1-2\sqrt[]{x}+6⋮\sqrt[]{x}-3\)

\(\Leftrightarrow7⋮\sqrt[]{x}-3\)

\(\Leftrightarrow\sqrt[]{x}-3\in U\left(7\right)=\left\{-1;1;-7;7\right\}\)

\(\Leftrightarrow x\in\left\{4;16;100\right\}\)

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\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}=\dfrac{1}{4}-\dfrac{1}{20}=\dfrac{4}{20}=\dfrac{1}{5}\)

45+45=90

12+78=90

45 + 45 = 900

12 + 78 = 90 

~ Ủng hộ mk nhé các bạn ~

45 + 45 = 90

12 + 78 = 90

k mk nha

Bn cần bài nào trong 2 bài nhỉ?

e tách câu hỏi ra nhe tạm thời cj giúp mụt câu nhe

a: \(=\dfrac{-5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+1+\dfrac{5}{7}=\dfrac{-5}{7}+1+\dfrac{5}{7}=1\)

b: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}\cdot4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{13}{56}\)

c: \(=\dfrac{2}{3}+\dfrac{1}{3}\cdot\dfrac{-24+45}{54}\cdot\dfrac{12}{7}\)

\(=\dfrac{2}{3}+\dfrac{1}{3}\cdot\dfrac{21}{54}\cdot\dfrac{12}{7}=\dfrac{2}{3}+\dfrac{2}{9}=\dfrac{6+2}{9}=\dfrac{8}{9}\)

d: \(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{107}-\dfrac{1}{111}\)

\(=\dfrac{1}{3}-\dfrac{1}{111}=\dfrac{108}{333}=\dfrac{12}{37}\)

II

1 the most popular

2 more intelligent

3 the shortest

4 bigger than

5 more comfortable than

6 worse

7 more peaceful than

8 the cleverest

9 the most delicious

10 the most boring

11 the most intelligent

12 the oldest

13 more uncomfortable

14 more important

15 healthier

16 the most difficult

17 most expensive

18 faster 

19 more interesting

20 earlier

III

1 Gray is taller than Rick

2 John has got new light trousers

3 Mary likes bigger clothes

4 Rick is wearing an expensive coat

5 Carol has got the shortest scraft

6 He is the tallest student

7 Mary was the most ppular actress

8 He was the best football player

9 Mary play better than you

10 Your father is stronger than mine