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11 tháng 2 2019

\(\left(2x+3\right)\left(\dfrac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\dfrac{3x+8}{2-7x}+1\right)\)

ĐK: \(x\ne\dfrac{2}{7}\)

\(\Leftrightarrow\left(2x+3\right)\left(3x+8+2-7x\right)=\left(x-5\right)\left(3x+8+2-7x\right)\\ \Leftrightarrow\left(2x+3\right)\left(10-4x\right)=\left(x-5\right)\left(10-4x\right)\\ \Leftrightarrow\left(10-4x\right)\left(2x+3-x+5\right)=0\\ \Leftrightarrow\left(10-4x\right)\left(x+8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}10-4x=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\left(TM\right)\\x=-8\left(TM\right)\end{matrix}\right.\)

Vậy \(S=\left\{\dfrac{5}{2};-8\right\}\)

4 tháng 3 2018

(=)2x+3=x-5

(=)x+8=0

(=)x=-8

22 tháng 4 2017

Giải bài 52 trang 33 SGK Toán 8 Tập 2 | Giải toán lớp 8

Giải bài 52 trang 33 SGK Toán 8 Tập 2 | Giải toán lớp 8

4 tháng 2 2022

\(i.\dfrac{\left(2x+1\right)^2}{5}-\dfrac{\left(x-1\right)^2}{3}=\dfrac{7x^2-14x-5}{15}\)

\(\Leftrightarrow\dfrac{4x^2+4x+1}{5}-\dfrac{x^2-2x+1}{3}=\dfrac{7x^2-14x-5}{15}\)

\(\Leftrightarrow\dfrac{12x^2+12x+3}{15}-\dfrac{5x^2-10x+5}{15}=\dfrac{7x^2-14x-5}{15}\)

\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5=7x^2-14x-5\)

\(\Leftrightarrow36x=-3\)

\(\Leftrightarrow x=-\dfrac{1}{12}\)

4 tháng 2 2022

\(k.x+\dfrac{2x+\dfrac{x-1}{5}}{3}=1-\dfrac{3x-\dfrac{1-2x}{3}}{5}\)

\(\Leftrightarrow\dfrac{15x}{15}+\dfrac{10x+x-1}{15}=\dfrac{15}{15}-\dfrac{9x-1+2x}{15}\)

\(\Leftrightarrow15x+9x-1=14-7x\)

\(\Leftrightarrow31x=15\)

\(\Leftrightarrow x=\dfrac{15}{31}\)

28 tháng 5 2021

ĐK: ` x \ne 2/7`

`(2x+3)((3x+8)/(2-7x)+1)=(x-5)((3x+8)/(2-7x)+1)`

`<=> ((3x+8)(2-7x)+1)(2x+3-x+5)=0`

`<=> ((3x+8)/(2-7x)+1)(x+8)=0`

 \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3x+8}{2-7x}=-1\\x+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-8\end{matrix}\right.\)

Vậy `S={5/2 ; -8}`.

28 tháng 5 2021

khó hiểu lắm bạn ơii:<

b: \(\Leftrightarrow\dfrac{7x+10}{x+1}\left(x^2-x-2-2x^2+3x+5\right)=0\)

\(\Leftrightarrow\left(7x+10\right)\left(-x^2+2x+3\right)=0\)

\(\Leftrightarrow\left(7x+10\right)\left(x^2-2x-3\right)=0\)

=>(7x+10)(x-3)=0

hay \(x\in\left\{-\dfrac{10}{7};3\right\}\)

d: \(\Leftrightarrow\dfrac{13}{2x^2+7x-6x-21}+\dfrac{1}{2x+7}-\dfrac{6}{\left(x-3\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\dfrac{13}{\left(2x+7\right)\left(x-3\right)}+\dfrac{1}{\left(2x+7\right)}-\dfrac{6}{\left(x-3\right)\left(x+3\right)}=0\)

\(\Leftrightarrow26x+91+x^2-9-12x-14=0\)

\(\Leftrightarrow x^2+14x+68=0\)

hay \(x\in\varnothing\)

b)

ĐKXĐ: \(x\notin\left\{2;3;\dfrac{1}{2}\right\}\)

Ta có: \(\dfrac{x+4}{2x^2-5x+2}+\dfrac{x+1}{2x^2-7x+3}=\dfrac{2x+5}{2x^2-7x+3}\)

\(\Leftrightarrow\dfrac{x+4}{\left(x-2\right)\left(2x-1\right)}+\dfrac{x+1}{\left(x-3\right)\left(2x-1\right)}=\dfrac{2x+5}{\left(2x-1\right)\left(x-3\right)}\)

\(\Leftrightarrow\dfrac{\left(x+4\right)\left(x-3\right)}{\left(x-2\right)\left(2x-1\right)\left(x-3\right)}+\dfrac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)\left(2x-1\right)}=\dfrac{\left(2x+5\right)\left(x-2\right)}{\left(2x-1\right)\left(x-3\right)\left(x-2\right)}\)

Suy ra: \(x^2-3x+4x-12+x^2-2x+x-2=2x^2-4x+5x-10\)

\(\Leftrightarrow2x^2-14=2x^2+x-10\)

\(\Leftrightarrow2x^2-14-2x^2-x+10=0\)

\(\Leftrightarrow-x-4=0\)

\(\Leftrightarrow-x=4\)

hay x=-4(nhận)

Vậy: S={-4}

12 tháng 8 2021

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a: =>10x-4=15-9x

=>19x=19

hay x=1

b: \(\Leftrightarrow3\left(10x+3\right)=36+4\left(8x+6\right)\)

=>30x+9=36+32x+24

=>30x-32x=60-9

=>-2x=51

hay x=-51/2

c: \(\Leftrightarrow2x+\dfrac{6}{5}=5-\dfrac{13}{5}-x\)

=>3x=6/5

hay x=2/5

d: \(\Leftrightarrow\dfrac{7x}{8}-\dfrac{5\left(x-9\right)}{1}=\dfrac{20x+1.5}{6}\)

\(\Leftrightarrow21x-120\left(x-9\right)=4\left(20x+1.5\right)\)

=>21x-120x+1080=80x+60

=>-179x=-1020

hay x=1020/179

e: \(\Leftrightarrow5\left(7x-1\right)+60x=6\left(16-x\right)\)

=>35x-5+60x=96-6x

=>95x+6x=96+5

=>x=1

f: \(\Leftrightarrow6\left(x+4\right)+30\left(-x+4\right)=10x-15\left(x-2\right)\)

=>6x+24-30x+120=10x-15x+30

=>-24x+96=-5x+30

=>-19x=-66

hay x=66/19

21 tháng 1 2022

1, <=> 3x-1-2x=6 <=> x =7 

2, (2x-1)(7-x)=x^2-7x

<=> 14x -2x^2-7+x=x^2-7x

<=> -3x^2+ 15x - 7 = -7x 

<=> -3x^2 +23x - 7 =0

<=> \(x=\dfrac{23\pm\sqrt{445}}{6}\)

NV
21 tháng 1 2022

1.

\(\Leftrightarrow3x-1-2x=6\)

\(\Leftrightarrow x-1=6\)

\(\Leftrightarrow x=7\)

2.

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

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

\(\Leftrightarrow\left(7-x\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}7-x=0\\3x-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=\dfrac{1}{3}\end{matrix}\right.\)