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17 tháng 2 2019
\(\Leftrightarrow\frac{5\left(x+5\right)-3\left(x-3\right)}{15}=\frac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Leftrightarrow\frac{2x+34}{15}=\frac{2x+34}{x^2+2x-15}\Leftrightarrow\orbr{\begin{cases}2x+34=0\\x^2+2x-15=15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-17\\x^2+2x-30=0\end{cases}}\)
Từ đó tìm được \(S=\left\{-17;\sqrt{31}-1;-\sqrt{31}-1\right\}\)
6 tháng 2 2020
\(b,\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x-\frac{x-3}{2}}{5}-x+1\)
\(\Leftrightarrow\frac{2x}{15}-\frac{4-3x}{75}=\frac{7x}{5}-\frac{x-3}{10}-x+1\)
\(\Leftrightarrow\frac{10.2x}{150}-\frac{2\left(4-3x\right)}{150}=\frac{30.7x}{150}-\frac{15\left(x-3\right)}{150}-\frac{150\left(x-1\right)}{150}\)
\(\Leftrightarrow2x-8+6x=210x-15x+45-150x+150\)
\(\Leftrightarrow-19x=203\)
\(\Leftrightarrow x=-\frac{203}{19}\)
Vậy ............
16 tháng 3 2023
a:=>x^2-1-x=2x-1
=>x^2-x-1=2x-1
=>x^2-3x=0
=>x=0(loại) hoặc x=3(nhận)
b:=>x+2=0 hoặc 5-3x=0
=>x=-2 hoặc x=5/3
c:=>20(1-2x)+6x=9(x-5)-24
=>20-40x+6x=9x-45-24
=>-34x+20=9x-69
=>-43x=-89
=>x=89/43
d: =>x^2+4x+4-x^2-2x+3=2x^2+8x-4x-16-3
=>2x^2+4x-19=-2x+7
=>2x^2+6x-26=0
=>x^2+3x-13=0
=>\(x=\dfrac{-3\pm\sqrt{61}}{2}\)
e: =>(2x-3)(2x-3-x-1)=0
=>(2x-3)(x-4)=0
=>x=4 hoặc x=3/2
AL
17 tháng 2 2019
a) \(\dfrac{x+5}{3}-\dfrac{x-3}{5}=\dfrac{5}{x-3}-\dfrac{3}{x+5}\)
\(\Rightarrow\dfrac{5\left(x+5\right)}{15}-\dfrac{3\left(x-3\right)}{15}=\dfrac{5\left(x+5\right)}{\left(x-3\right)\left(x+5\right)}-\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Rightarrow\dfrac{5\left(x+5\right)-3\left(x-3\right)}{15}=\dfrac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
* Với \(5\left(x+5\right)-3\left(x-3\right)=0\),
Ta có được đẳng thức đúng
=> 5x + 25 - 3x + 9 = 0
=> 2x + 34 = 0
=> 2x = -34
=> x = -17
* Với 5( x+5 ) - 3 (x-3 ) \(\ne\)0, ta có
\(\dfrac{5\left(x+5\right)-3\left(x-3\right)}{15}=\dfrac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Rightarrow\dfrac{1}{15}=\dfrac{1}{\left(x-3\right)\left(x+5\right)}\)
\(\Rightarrow\left(x-3\right)\left(x+5\right)=15\)
\(\Rightarrow x^2+5x-3x-15-15=0\)
\(\Rightarrow x^2+2x-30=0\)
=> \(\left(x+1-\sqrt{31}\right)\left(x+1+\sqrt{31}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-1+\sqrt{31}\\x=-1-\sqrt{31}\end{matrix}\right.\)
17 tháng 2 2019
\(a)\dfrac{x+5}{3}-\dfrac{x-3}{5}=\dfrac{5}{x-3}-\dfrac{3}{x+5}\)(ĐKXĐ: \(x\ne3,x\ne-5\))
\(\Leftrightarrow\dfrac{x+5}{3}-\dfrac{x-3}{5}-\dfrac{5}{x-3}+\dfrac{3}{x+5}=0\\ \Leftrightarrow\dfrac{5\left(x-3\right)\left(x+5\right)^2-3\left(x-3\right)^2\left(x+5\right)-75\left(x+5\right)+45\left(x-3\right)}{15\left(x-3\right)\left(x+5\right)}=0\\ \Leftrightarrow\dfrac{2x^3+38x^2+8x-1020}{15\left(x-3\right)\left(x+5\right)}=0\\ \Leftrightarrow2x^3+38x^2+8x-1020=0\\ \Leftrightarrow\left(x+17\right)\left(x^2+2x-30\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+17=0\\x^2+2x-30=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-17\left(TM\right)\\x=-1+\sqrt{31}\left(TM\right)\\x=-1-\sqrt{31}\left(TM\right)\end{matrix}\right.\)
Vậy....
H
16 tháng 3 2023
\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
\(\Leftrightarrow\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x\left(x+1\right)}\)
ĐKXĐ : \(\left\{{}\begin{matrix}x\ne0\\x+1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne-1\end{matrix}\right.\)
Ta có : `(x-1)/x -1/(x+1) =(2x-1)/(x(x+1))`
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}-\dfrac{x}{x\left(x+1\right)}=\dfrac{2x-1}{x\left(x+1\right)}\)
`=> x^2 +x -x-1 -x-2x+1=0`
`<=> x^2 -3x =0`
`<=> x(x-3)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=3\end{matrix}\right.\)
__
`(x+2)(5-3x)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\5-3x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\3x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{5}{3}\end{matrix}\right.\)
__
\(\dfrac{5\left(1-2x\right)}{3}+\dfrac{x}{2}=\dfrac{3\left(x-5\right)}{4}-2\)
\(\Leftrightarrow\dfrac{20\left(1-2x\right)}{12}+\dfrac{6x}{12}=\dfrac{9\left(x-5\right)}{12}-\dfrac{24}{12}\)
`<=> 2x- 40x + 6x = 9x - 45 -24`
`<=> 2x- 40x + 6x-9x + 45 +24=0`
`<=>-41x+69=0`
`<=>-41x=-69`
`<=> x=69/41`
13 tháng 1 2016
khó quá mk mới học lớp 6 nên k giải đc thông cảm cho mk nha
24 tháng 1 2022
f: =>35x-5=96-6x
=>41x=101
hay x=101/41
g: =>3(x-3)=90-5(1-2x)
=>3x-9=90-5+10x
=>3x-9=10x+85
=>-7x=94
hay x=-94/7
25 tháng 1 2022
h.3x - 2/6 - 5 = 3 - 2(x + 7)/4
<=> 3x - 2 - 30/6 = 3 - 2(x + 7)/4
<=> 3x - 32/6 = 3 - 2x - 14/4
<=> 3x - 32/6 = -2x - 11/4
<=> 6x - 64/12 = -6x - 33/12
<=> 6x - 64 = -6x - 33 <=> 12x = 31 <=> x = 31/12
\(\Leftrightarrow x+\frac{11x-1}{\frac{5}{3}}=1-\frac{3x-6x^2}{\frac{3}{5}}\)\(\Leftrightarrow x+\frac{11x-1}{15}=1-\frac{3x-6x^2}{15}\)\(\Leftrightarrow\frac{26x-1}{15}=\frac{15-3x+6x^2}{15}\)\(\Leftrightarrow26x-1=15-3x+6x^2\)\(\Leftrightarrow6x^2-29x+16=0\)\(\Leftrightarrow6x^2-2\cdot\sqrt{6}\cdot\frac{29}{2\sqrt{6}}+\left(\frac{29}{2\sqrt{6}}\right)^2-\frac{697}{24}=0\)\(\Leftrightarrow\left(\sqrt{6}x-\frac{29}{2\sqrt{6}}\right)^2=\frac{697}{24}\)\(\Leftrightarrow\orbr{\begin{cases}\sqrt{6}x-\frac{29}{2\sqrt{6}}=\sqrt{\frac{697}{24}}\\\sqrt{6}x-\frac{29}{2\sqrt{6}}=-\sqrt{\frac{697}{24}}\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{29+\sqrt{457}}{12}\\x=\frac{29-\sqrt{457}}{12}\end{cases}}\)