`15)(-5sqrtx+4)/(3sqrtx-2)+(6sqrtx+4)/(2sqrtx+3)+(29sqrtx-28)/(3(6x+5sqrtx-6))`
`=(3(-5sqrtx+4)(2sqrtx+3)+3(6sqrtx+4)(3sqrtx-2)+29sqrtx-28)/(3(3sqrtx-2)(2sqrtx+3))`
`=(-30x-21sqrtx+36+54x-24+29sqrtx-28)/(3(3sqrtx-2)(2sqrtx+3))`
`=(24x+8sqrtx-16)/(3(3sqrtx-2)(2sqrtx+3))`

`=(8(3sqrtx-2)(sqrtx+1))/(3(3sqrtx-2)(2sqrtx+3))`

`=(8(sqrtx+1))/(3(2sqrtx+3))`

thank

8: Ta có: \(\dfrac{\sqrt{x}-3}{\sqrt{x}-2}-\dfrac{2\sqrt{x}-1}{\sqrt{x}-1}+\dfrac{x-2}{x-3\sqrt{x}+2}\)

\(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}-\dfrac{\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}+\dfrac{x-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{x-4\sqrt{x}+3-2x+4\sqrt{x}+\sqrt{x}-2+x-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

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

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

`16)(2sqrtx-4)/(3sqrtx-4)-(4+2sqrtx)/(sqrtx-2)+(x+13sqrtx-20)/(3x-10sqrtx+8)`
`=((2sqrtx-4)(sqrtx-2)-(4+2sqrtx)(3sqrtx-4)+x+13sqrtx-20)/((3sqrtx-4)(sqrtx-2)`
`=(2x-8sqrtx+8-6x-4sqrtx+16+x+13sqrtx-20)/((3sqrtx-4)(sqrtx-2)`
`=(-3x+sqrtx+4)/((3sqrtx-4)(sqrtx-2)`
`=(-(3sqrtx-4)(sqrtx+1))/((3sqrtx-4)(sqrtx-2)`
`=(-(sqrtx+1))/(sqrtx-2)`

thank

18: Ta có: \(\dfrac{\sqrt{x}\left(16-\sqrt{x}\right)}{x-4}+\dfrac{3+2\sqrt{x}}{2-\sqrt{x}}-\dfrac{2-3\sqrt{x}}{\sqrt{x}+2}\)

\(=\dfrac{16\sqrt{x}-x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\left(3+2\sqrt{x}\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\left(2-3\sqrt{x}\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{16\sqrt{x}-x-3\sqrt{x}-6-2x-4\sqrt{x}-2\sqrt{x}+4+3x-6\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{3\sqrt{x}-2}{x-4}\)

Số số hạng là: (19-11)*1+1=9(số hạng) 

Có số cặp số là:9:2=4 dư 1

Vậy có 4 cặp và dư 1 số

Ta có : 11+(12+19)+(13+18)+(14+17)+(15+16)

=11+21+21+21+21

=11+(21.4)

=11+84

=95

11+12+13+14+15+16+17+18+19=(11+19)+(12+18)+(13+17)+(16+14)+15    

                                                     =30+30+30+30+15

                                                      =30*4+15                                                

                                                      =120+15                                              

                                                      =135 

11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19

= ( 11 + 19 ) + ( 12 + 18 ) + ( 13 + 17 ) + ( 14 + 16 ) + 15

= 30 + 30 + 30 + 30 + 15

= 135

16. \(\dfrac{2\sqrt{x}-4}{3\sqrt{x}-4}-\dfrac{4+2\sqrt{x}}{\sqrt{x}-2}+\dfrac{x+13\sqrt{x}-20}{3x-10\sqrt{x}+8}\)

=\(\dfrac{\left(2\sqrt{x}-4\right)\left(\sqrt{x}-2\right)-\left(4+2\sqrt{x}\right)\left(3\sqrt{x}-4\right)+x+13\sqrt{x}-20}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)

=\(\dfrac{2x-8\sqrt{x}+8-\left(4\sqrt{x}+6x-16\right)+x+13\sqrt{x}-20}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)

=​\(\dfrac{2x-8\sqrt{x}+8-4\sqrt{x}-6x+16+x+13\sqrt{x}-20}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)​​​

=\(\dfrac{-3x+\sqrt{x}+4}{\left(3\sqrt{x}-4\right)\left(x+2\right)}\)

=\(\dfrac{-\left(3x+3\sqrt{x}-4\sqrt{x}-4\right)}{\left(3\sqrt{x}-4\right)\left(x+2\right)}\)

=\(\dfrac{-\left(3\sqrt{x}-4\right)\left(\sqrt{x}+1\right)}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}+2\right)}\)=\(\dfrac{-\sqrt{x}-1}{\sqrt{x}+2}\)

14.

=\(\dfrac{-\left(7\sqrt{x}+7\right)\left(\sqrt{x}+2\right)}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)+\(\dfrac{\left(2\sqrt{x}-2\right)\left(5\sqrt{x}-1\right)}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)+\(\dfrac{39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

=\(\dfrac{-7x-21\sqrt{x}-14}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)+\(\dfrac{10x-12\sqrt{x}+2}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)+​​​​​​\(\dfrac{39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)​​​​​​​​

=\(\dfrac{-7x-21\sqrt{x}-14+10x-12\sqrt{x}+2+39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

=\(\dfrac{3x-6\sqrt{x}}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)=\(\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

17.

\(\dfrac{3}{1-\sqrt{2}}+\dfrac{\sqrt{2}-1}{\sqrt{2}+1}=\dfrac{3\left(\sqrt{2}+1\right)-\left(\sqrt{2}-1\right)^2}{-1}=-\left(3\sqrt{2}+3-3+2\sqrt{2}\right)=-5\sqrt{2}\)

\(\dfrac{\sqrt{5}-1}{\sqrt{5}+1}+\dfrac{6}{1-\sqrt{5}}=\dfrac{\left(\sqrt{5}-1\right).\left(1-\sqrt{5}\right)+6.\left(\sqrt{5}+1\right)}{-4}=\dfrac{6-2\sqrt{5}-6\sqrt{5}-6}{4}=\dfrac{-8\sqrt{5}}{4}=-2\sqrt{5}\)

\(\dfrac{\sqrt{2}-\sqrt{3}}{2-\sqrt{6}}+\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{6}+2}=\dfrac{\left(\sqrt{2}-\sqrt{3}\right).\left(\sqrt{6}+2\right)+\left(\sqrt{3}-\sqrt{2}\right).\left(2-\sqrt{6}\right)}{-2}=\dfrac{2\left(\sqrt{12}-\sqrt{18}\right)}{-2}=\sqrt{18}-\sqrt{12}\)

\(\dfrac{-31+8\sqrt{x}-x}{x-8\sqrt{x}+15}-\dfrac{\sqrt{x}+5}{\sqrt{x}-3}-\dfrac{3\sqrt{x}-1}{5-\sqrt{x}}\)

\(=\dfrac{-31+8\sqrt{x}-x}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-3\right)}-\dfrac{\sqrt{x}+5}{\sqrt{x}-3}+\dfrac{3\sqrt{x}-1}{\sqrt{x}-5}\)

\(=\dfrac{-31+8\sqrt{x}-x-x+25+3x-9\sqrt{x}-\sqrt{x}+3}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-3\right)}=\dfrac{x-2\sqrt{x}-3}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-3\right)}=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}-5}\)

11.

\(=\frac{\sqrt{x}-3}{2-\sqrt{x}}+\frac{\sqrt{x}-2}{3+\sqrt{x}}+\frac{9-x}{(2-\sqrt{x})(\sqrt{x}+3)}\)

\(=\frac{(\sqrt{x}-3)(\sqrt{x}+3)}{(2-\sqrt{x})(\sqrt{x}+3)}+\frac{\sqrt{x}-2}{3+\sqrt{x}}+\frac{9-x}{(2-\sqrt{x})(\sqrt{x}+3)}\)

\(=\frac{x-9}{(2-\sqrt{x})(\sqrt{x}+3)}+\frac{\sqrt{x}-2}{3+\sqrt{x}}+\frac{9-x}{(2-\sqrt{x})(\sqrt{x}+3)}\)

\(=\frac{\sqrt{x}-2}{3+\sqrt{x}}\)

12.

\(=\frac{(3-\sqrt{x})(3\sqrt{x}-2)+(5\sqrt{x}+7)(3\sqrt{x}+4)}{(5\sqrt{x}+7)(3\sqrt{x}-2)}-\frac{42\sqrt{x}+34}{(5\sqrt{x}+7)(3\sqrt{x}-2)}\) 

\(=\frac{12x+52\sqrt{x}+22}{(5\sqrt{x}+7)(3\sqrt{x}-2)}-\frac{42\sqrt{x}+34}{(5\sqrt{x}+7)(3\sqrt{x}-2)}\)

\(=\frac{12x+10\sqrt{x}-12}{(5\sqrt{x}+7)(3\sqrt{x}-2)}=\frac{2(3\sqrt{x}-2)(2\sqrt{x}+3)}{(5\sqrt{x}+7)(3\sqrt{x}-2)}=\frac{2(2\sqrt{x}+3)}{5\sqrt{x}+7}\)

13.

\(=\frac{(\sqrt{x}+2)(2\sqrt{x}-3)+(3\sqrt{x}-4)(-\sqrt{x}+2)}{(-\sqrt{x}+2)(2\sqrt{x}-3)}+\frac{-7\sqrt{x}+10}{(-\sqrt{x}+2)(2\sqrt{x}-3)}\)

\(=\frac{-x+11\sqrt{x}-14}{(-\sqrt{x}+2)(2\sqrt{x}-3)}+\frac{-7\sqrt{x}+10}{(-\sqrt{x}+2)(2\sqrt{x}-3)}\)

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

14, \(\frac{-7\sqrt{x}+7}{5\sqrt{x}-1}+\frac{2\sqrt{x}-2}{\sqrt{x}+2}+\frac{39\sqrt{x}+12}{5x+9\sqrt{x}-2}\)

\(=\frac{-7\sqrt{x}+7}{5\sqrt{x}-1}+\frac{2\sqrt{x}-2}{\sqrt{x}+2}+\frac{39\sqrt{x}+12}{\left(\sqrt{x}+2\right)\left(5\sqrt{x}-1\right)}\)

\(=\frac{\left(-7\sqrt{x}+7\right)\left(\sqrt{x}+2\right)+\left(2\sqrt{x}-2\right)\left(5\sqrt{x}-1\right)+39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{-7x-14\sqrt{x}+7\sqrt{x}+14+10x-2\sqrt{x}-10\sqrt{x}+2+39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3x+20\sqrt{x}+28}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{\left(3\sqrt{x}+14\right)\left(\sqrt{x}+2\right)}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3\sqrt{x}+14}{5\sqrt{x}-1}\)

thank

Bài 1

415- 2*(x -19)-15=20

<=> 415 - 2x + 38 - 15 = 20

<=> 438 -2x = 20

<=> 2x = 418

<=> x = 209

5*x-14+x=100+4*x 

<=> 6x- 14 = 100 + 4x

<=> 2x = 114

<=> x = 57

415-2(x-19)-15=20

415-2x+38-15=20

(415+38-15)-2x=20

438-2x=20

       2x=438-20

       2x=418

         x=418:2

         x=204

5x-14+x=100+4x

5x+x-4x=100+14

         2x=114

           x=114:2

           x=57

\(415-2.\left(x-19\right)-15=20\)

\(\Leftrightarrow400-2.\left(x-19\right)=20\)

\(\Leftrightarrow2.\left(x-19\right)=380\)

\(\Leftrightarrow x-19=190\)

\(\Leftrightarrow x=209\)

    \(5x-14+x=100+4x\)

\(\Leftrightarrow6x-14=100+4x\)

\(\Leftrightarrow6x-4x=100+14\)

\(\Leftrightarrow2x=114\)

\(\Leftrightarrow x=57\)

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