b: \(\Leftrightarrow\dfrac{20}{x}-\dfrac{20}{x+20}=\dfrac{1}{6}\)

=>\(\dfrac{20x+400-20x}{x\left(x+20\right)}=\dfrac{1}{6}\)

=>x*(x+20)=400*6=2400

=>x^2+20x-2400=0

=>(x+60)(x-40)=0

=>x=-60 hoặc x=40

c: \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{4x^2-1}\)

=>(2x+1)^2-(2x-1)^2=8

=>4x^2+4x+1-4x^2+4x-1=8

=>8x=8

=>x=1(nhận)

`100/x-100/(x+10)=1/2`
`<=>(100x+1000-100x)/(x^2+10x)=1/2`
`<=>1000/(x^2+10x)=1/2`
`<=>x^2+10x=2000`
`<=>x^2+10x-2000=0`
`Delta'=25+2000=2025`
`<=>x_1=40,x_2=-50`
Vậy `S={40,-50}`

\(\dfrac{100}{x}=\dfrac{1}{2}+\dfrac{100}{x+10}\Rightarrow\dfrac{100}{x}=\dfrac{x+210}{2x+20}\Rightarrow200x+2000=x^2+210x\)

\(x^2+10x-2000=0\Leftrightarrow\left(x+50\right)\left(x-40\right)=0\Rightarrow x=40\)

ĐK: ` x\ne 0; x \ne -100`

`4800/x-4800/(x+100)=8`

`<=>1/x-1/(x+100) =1/600`

`<=> (x+100-x)/(x(x+100) = 1/600`

`<=> 100/(x(x+100))=1/600`

`<=> x^2+100x = 60000`

\(\left[{}\begin{matrix}x=200\\x=-300\end{matrix}\right.\)

Vậy...

`4800/x-4800/(x+10)=8`

`ĐK:x ne 0,x ne -10`

`pt<=>600/x-600/(x+10)=1`

`<=>(600x+6000-600x)/(x^2+10x)=1`

`<=>6000/(x^2+10x)=1`

`<=>x^2+10x=6000`

`<=>x^2+10x-6000=0`

`Delta'=25+6000=6025`

`<=>x_1=20,x_2=-30`

a: \(\Leftrightarrow\left(\dfrac{x+2001}{5}+1\right)+\left(\dfrac{x+1999}{7}+1\right)+\left(\dfrac{x+1997}{9}+1\right)+\left(\dfrac{x+1995}{11}+1\right)=0\)

=>x+2006=0

=>x=-2006

b: \(\Leftrightarrow\left(\dfrac{x-15}{100}-1\right)+\left(\dfrac{x-10}{105}-1\right)+\left(\dfrac{x-100}{5}-1\right)=\left(\dfrac{x-100}{15}-1\right)+\left(\dfrac{x-105}{10}-1\right)+\left(\dfrac{x-110}{5}-1\right)\)

=>x-105=0

=>x=105

ĐKXĐ: \(x\notin\left\{0;-20\right\}\)

\(\left\{{}\begin{matrix}y=20+x\\\dfrac{100}{x}-\dfrac{100}{20+x}=\dfrac{5}{6}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\\dfrac{20}{x}-\dfrac{20}{x+20}=\dfrac{1}{6}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\\dfrac{20x+400-20x}{x\left(x+20\right)}=\dfrac{1}{6}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\\dfrac{400}{x\left(x+20\right)}=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x+20\\x\left(x+20\right)=2400\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\x^2+20x-2400=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\\left(x+60\right)\left(x-40\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x+20\\\left[{}\begin{matrix}x+60=0\\x-40=0\end{matrix}\right.\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=x+20\\x\in\left\{-60;40\right\}\end{matrix}\right.\)(nhận)

=>\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-60\\y=x+20=-60+20=-40\end{matrix}\right.\\\left\{{}\begin{matrix}x=40\\y=x+20=60\end{matrix}\right.\end{matrix}\right.\)

\(\dfrac{200x}{100}+\dfrac{300\left(x-20\right)}{100}=\dfrac{33.500}{100}\)

=> 200x + 300(x - 20) = 16500

<=> 200x + 300x - 6000 = 16500

<=> 500x = 22500

<=> x = 45

S = {45}

Ta có: \(\dfrac{x\cdot200}{100}+\dfrac{\left(x-20\right)\cdot300}{100}=\dfrac{33\cdot500}{100}\)

\(\Leftrightarrow200x+300x-6000=16500\)

\(\Leftrightarrow500x=22500\)

hay x=45

Vậy: S={45}

1)

\(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)

\(\Leftrightarrow\dfrac{x-5}{100}+1+\dfrac{x-4}{101}+1+\dfrac{x-3}{102}+1=\dfrac{x-100}{5}+1+\dfrac{x-101}{4}+1+\dfrac{x-102}{3}+1\)

\(\Leftrightarrow\dfrac{x-105}{100}+\dfrac{x-105}{101}+\dfrac{x-105}{102}=\dfrac{x-105}{5}+\dfrac{x-105}{4}+\dfrac{x-105}{3}+\dfrac{x-105}{2}\)

\(\Leftrightarrow\dfrac{x-105}{100}+\dfrac{x-105}{101}+\dfrac{x-105}{102}-\dfrac{x-105}{5}-\dfrac{x-105}{4}-\dfrac{x-105}{3}-\dfrac{x-105}{2}=0\)

\(\Leftrightarrow\left(x-105\right)\left(\dfrac{1}{100}+\dfrac{1}{101}+\dfrac{1}{102}-\dfrac{1}{5}-\dfrac{1}{4}-\dfrac{1}{3}-\dfrac{1}{2}\right)=0\)\(\Leftrightarrow105-x=0\)

\(\Leftrightarrow x=105\)

b)

\(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=0\)

\(\Leftrightarrow\dfrac{29-x}{21}+1+\dfrac{27-x}{23}+1+\dfrac{25-x}{25}+1+\dfrac{23-x}{27}+1+\dfrac{21-x}{29}+1=0\)

\(\Leftrightarrow\dfrac{50-x}{21}+\dfrac{50-x}{23}+\dfrac{50-x}{25}+\dfrac{20-x}{27}+\dfrac{50-x}{29}=0\)

\(\Leftrightarrow\left(50-x\right)\left(\dfrac{1}{21}+\dfrac{1}{23}+\dfrac{1}{25}+\dfrac{1}{27}+\dfrac{1}{29}\right)=0\)

\(\Leftrightarrow50-x=0\)

\(\Leftrightarrow x=50\)

2)

\(\left(5x+1\right)^2=\left(3x-2\right)^2\)

\(\Leftrightarrow\left|5x+1\right|=\left|3x-2\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}5x+1=3x-2\\5x+1=-3x+2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=\dfrac{1}{8}\end{matrix}\right.\)

b) \(\left(x+2\right)^3=\left(2x+1\right)^3\)

\(\Leftrightarrow x^3+6x^2+12x+8=8x^3+12x^2+6x+1\)

\(\Leftrightarrow-7x^3-6x^2+6x+7=0\)

\(\Leftrightarrow-7x^3+7x^2-13x^2+13x-7x+7=0\)

\(\Leftrightarrow-7x^2\left(x-1\right)-13x\left(x-1\right)-7\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(-7x^2-13x-7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\-7x^2-13x-7=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\-7\left(x^2+\dfrac{13}{7}x+1\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\-7\left(x+\dfrac{13}{14}\right)^2-\dfrac{169}{196}=0\left(l\right)\end{matrix}\right.\)

\(\Leftrightarrow x=1\)

c. \(\left(x+3\right)^4+\left(x+5\right)^4=2\)

Đặt: \(y=x+4\), ta có:

\(\left(y-1\right)^4+\left(y+1\right)^4=2\)

\(\Leftrightarrow y^4-4y^3+6y^2-4y+1+y^4+4y^3+6y^2+4y+1=2\)

\(\Leftrightarrow2y^4+12y^2=0\)

\(\Leftrightarrow2y^2\left(y^2+6\right)=0\)

\(\Leftrightarrow y=0\)

\(\Leftrightarrow x=-4\)

d) \(x^4-3x^3+4x^2-3x+1=0\)

\(\Leftrightarrow x^4-x^3-2x^3+2x^2+2x^2-2x-x+1=0\)

\(\Leftrightarrow x^3\left(x-1\right)-2x^2\left(x-1\right)+2x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2+2x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3-x^2-x^2+x+x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)\right]=0\)

\(\Leftrightarrow\left(x-1\right)^2\left(x^2-x+1\right)=0\)

\(\Leftrightarrow x=1\)

\(\dfrac{x-130}{20}\)+\(\dfrac{x-100}{25}\)+\(\dfrac{x-60}{30}\)+\(\dfrac{x-10}{35}\)=10

⇔\(\dfrac{2625\left(x-130\right)}{52500}\)+\(\dfrac{2100\left(x-100\right)}{52500}\)+\(\dfrac{1750\left(x-60\right)}{52500}\)+\(\dfrac{1500\left(x-10\right)}{52500}\)=\(\dfrac{525000}{52500}\)

⇔2625\(x\)-341250+2100\(x\)-210000+1750\(x\)-105000+1500\(x\)-15000=525000

⇔ 7975\(x\) = 1196250

⇔ \(x\) = \(\dfrac{1196250}{7975}\)

⇔\(x \) = 150

`1/x+1/(x+2)=5/12`

ĐK:`x ne 0,x ne -2`

`<=>(x+2+x)/(x^2+2x)=5/12`

`<=>(2x+2)/(x^2+2x)=5/12`

`<=>24x+24=5x^2+10x`

`<=>5x^2-14x-24=0`

Ta có:`Delta'=49+24.5`

`=49+120=169`

`=>x_1=-6/5,x_2=4`

Vậy `S={4,-6/5}`

$ĐKXĐ : x \neq 0, x \neq -2$

Ta có : $\dfrac{1}{x} + \dfrac{1}{x+2} = \dfrac{5}{12}$

$\to \dfrac{2x+2}{x.(x+2)} = \dfrac{5}{12}$

$\to (2x+2).12 = x.(x+2).5$

$\to 24x + 24 = 5x^2 + 10x$

$\to 5x^2 - 14x - 24 = 0 $

$\to (x-4).(5x+6) = 0 $

S\to$ \(\left[{}\begin{matrix}x=4\\x=-\dfrac{6}{5}\end{matrix}\right.\)  ( thỏa mãn ĐKXĐ )

Vậy :....