\(a,=\dfrac{\sqrt{2}\left(1+\sqrt{2}\right)}{1+\sqrt{2}}=\sqrt{2}\\ b,=\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=\sqrt{5}\\ c,=\dfrac{\sqrt{3}\left(1-\sqrt{2}\right)}{2\left(\sqrt{2}-1\right)}=-\dfrac{\sqrt{3}}{2}\\ d,=\dfrac{\sqrt{5}\left(1-\sqrt{2}\right)}{\sqrt{3}\left(1-\sqrt{2}\right)}=\dfrac{\sqrt{5}}{\sqrt{3}}=\dfrac{\sqrt{15}}{3}\\ e,=\dfrac{\sqrt{7}\left(\sqrt{7}+1\right)}{\sqrt{7}+1}=\sqrt{7}\\ f,=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}=\sqrt{5}\\ g,=\dfrac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}=\sqrt{2}\\ h,=\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=\sqrt{5}\)

1: \(=\dfrac{\dfrac{x^2+y^2-2xy}{xy}}{\dfrac{x^2-y^2}{xy}}\)

\(=\dfrac{\left(x-y\right)^2}{xy}:\dfrac{\left(x-y\right)\left(x+y\right)}{xy}=\dfrac{x-y}{x+y}\)

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

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

`#3107.101107`

a,

\([(6.x - 39) \div3] .28 =5628\)

`\Rightarrow (6x - 39) \div 3 = 5628 \div 28`

`\Rightarrow (6x - 39) \div 3 = 201`

`\Rightarrow 6x - 39 = 201 . 3`

`\Rightarrow 6x - 39 = 603`

`\Rightarrow 6x = 42`

`\Rightarrow x = 42 \div 6`

`\Rightarrow x = 7`

Vậy, `x = 7`

b,

`5(7x - 45) = 2^3 . 5^2 - 3^2 . 20`

`\Rightarrow 5(7x - 45) = 8.5.5 - 9.4.5`

`\Rightarrow 5(7x - 45) = 5.(8.5 - 9.4)`

`\Rightarrow 5(7x - 45) = 5.(40 - 36)`

`\Rightarrow 7x - 45 = 5.(40 - 36) \div 5`

`\Rightarrow 7x - 45 = 4`

`\Rightarrow 7x = 49`

`\Rightarrow x = 7`

Vậy, `x = 7.`

\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{18\cdot19\cdot20}\)

\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+\frac{2}{18\cdot19\cdot20}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot20}\right)\)

\(B=\frac{1}{2}\cdot\frac{189}{380}=\frac{189}{760}\)

\(C=\frac{52}{1\cdot6}+\frac{52}{6\cdot11}+\frac{52}{11\cdot16}+...+\frac{52}{31\cdot36}\)

\(C=\frac{52}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{6}{31\cdot36}\right)\)

\(C=\frac{52}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{31}-\frac{1}{36}\right)\)

\(C=\frac{52}{5}\cdot\left(1-\frac{1}{36}\right)\)

\(C=\frac{91}{9}\)

Từ bản vẽ hình chiếu 1 ta vẽ được vật thể như sau

Từ bản vẽ hình chiếu 2 ta vẽ được vật thể như sau :

Bảng4.4: