Giải phương trình sau
\(\frac{3x-2}{3x-2}-\frac{2}{3x+2}=\frac{6x^2}{9x^2-4}\)
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22 tháng 4 2020
Bài làm
a) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x-4}\)
\(\Leftrightarrow\frac{3x+2}{3x-2}-\frac{6}{3x+2}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Leftrightarrow\frac{(3x+2)\left(3x+2\right)}{(3x-2)\left(3x+2\right)}-\frac{6\left(3x-2\right)}{(3x+2)\left(3x-2\right)}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Rightarrow\left(3x+2\right)^2-\left(18x-12\right)=9x^2\)
\(\Leftrightarrow9x^2+12x+4-18x+12x-9x^2=0\)
\(\Leftrightarrow6x+4=0\)
\(\Leftrightarrow x=-\frac{4}{6}\)
\(\Leftrightarrow x=-\frac{2}{3}\)
Vậy x = -2/3 là nghiệm.
23 tháng 4 2020
@Tao Ngu :))@ 9x-4 không tách thành (3x+4)(3x-4) được đâu bạn. Chỗ đó phải là: 9x2-4
Bài thiếu đkxđ của x \(\hept{\begin{cases}3x-2\ne0\\2+3x\ne0\end{cases}\Leftrightarrow\hept{\begin{cases}3x\ne2\\3x\ne-2\end{cases}\Leftrightarrow}\hept{\begin{cases}x\ne\frac{2}{3}\\x\ne\frac{-2}{3}\end{cases}\Leftrightarrow}x\ne\pm\frac{2}{3}}\)
26 tháng 4 2021
a, \(\left|2x-1\right|-7=0\Leftrightarrow\left|2x-1\right|=7\)
Với \(x\ge\frac{1}{2}\)phương trình có dạng :
\(2x-1=7\Leftrightarrow x=4\)( tm )
Với \(x< \frac{1}{2}\)phương trình có dạng :
\(-2x+1=7\Leftrightarrow x=-3\)( tm )
Vậy tập nghiệm của phương trình là S = { -3 ; 4 }
26 tháng 4 2021
b, \(\frac{9x^2}{2\left(1-9x^2\right)}=\frac{3x}{6x-2}-\frac{1+9x}{3+9x}\)ĐK : \(x\ne\pm\frac{1}{3}\)
\(\Leftrightarrow-\frac{9x^2}{2\left(3x-1\right)\left(3x+1\right)}=\frac{3x}{2\left(3x-1\right)}-\frac{1+9x}{3\left(3x+1\right)}\)
\(\Leftrightarrow\frac{-27x^2}{6\left(3x-1\right)\left(3x+1\right)}=\frac{9x\left(3x+1\right)}{6\left(3x-1\right)\left(3x+1\right)}-\frac{2\left(1-9x\right)\left(3x+1\right)}{6\left(3x-1\right)\left(3x+1\right)}\)
\(\Leftrightarrow-27x^2=27x^2-9x-2\left(3x-27x^2\right)\)
\(\Leftrightarrow108x^2-15x=0\Leftrightarrow3x\left(36x-5\right)=0\Leftrightarrow x=0;x=\frac{5}{36}\)( tm )
Vậy tập nghiệm của phương trình là S = { 0 ; 5/36 }
A
15 tháng 4 2020
a, 2x-6=5x-9
=>2x-5x=-9+6
=>-3x=-3
=>x=1
b, 4x2-6x=0
=> 2x(2x-3)=0
=>x=0 hoặc x=\(\frac{3}{2}\)
c,
\(\frac{4+3x}{3}=\frac{x^2+1}{x}\\ =>\frac{4x+3x^2-3x^2-3}{x}=0\\ =>\frac{4x-3}{x}=0\\ =>4x-3=0\\ =>x=\frac{3}{4}\)
d,
\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x}{9x^2-4}\\ =>\left(3x+2\right)^2-6\left(3x-2\right)=9x\\ =>9x^2+12x+4-18x-12-9x=0\\ =>9x^2-15x+16=0\\ =>x=..\)
NV
18 tháng 4 2017
\(1.\frac{7x-3}{x-1}=\frac{2}{3}\) ( \(x\ne1\))
\(\Leftrightarrow\frac{3\left(7x-1\right)}{3\left(x-1\right)}=\frac{2\left(x-1\right)}{3\left(x-1\right)}\)
\(\Rightarrow3\left(7x-3\right)=2\left(x-1\right)\)
\(\Leftrightarrow21x-9=2x-2\)
\(\Leftrightarrow19x=7\)
\(\Leftrightarrow x=\frac{7}{19}\)
\(2.\frac{5x-1}{3x+2}=\frac{5x-7}{3x-1}\)
\(\Leftrightarrow\frac{\left(5x-1\right)\left(3x-1\right)}{\left(3x+2\right)\left(3x-1\right)}=\frac{\left(5x-7\right)\left(3x+2\right)}{\left(3x-1\right)\left(3x+2\right)}\)
\(\Rightarrow\left(5x-1\right)\left(3x-1\right)=\left(5x-7\right)\left(3x+2\right)\)
\(\Leftrightarrow15x^2-5x-3x+1=15x^2+10x-21x-14\)
\(\Leftrightarrow15x^2-8x+1=15x^2-11x-14\)
\(\Leftrightarrow\left(15x^2-15x^2\right)+\left(-8x+11x\right)=-14-1\)
\(\Leftrightarrow3x=-15\)
\(\Leftrightarrow x=-5\)
\(3.\frac{1-x}{x+1}+3=\frac{2x+3}{3x-1}\)
\(\Leftrightarrow\frac{\left(1-x\right)\left(3x-1\right)}{\left(x+1\right)\left(3x-1\right)}+\frac{3\left(x+1\right)\left(3x-1\right)}{\left(x+1\right)\left(3x-1\right)}=\frac{\left(2x+3\right)\left(x+1\right)}{\left(3x-1\right)\left(0+1\right)}\)
\(\Rightarrow\left(1-x\right)\left(3x-1\right)+3\left(x+1\right)\left(3x-1\right)=\left(2x+3\right)\left(x+1\right)\)
\(\Leftrightarrow3x-1-3x^2+x+3\left(3x^2-x+3x-1\right)=2x^2+2x+3x+3\)
\(\Leftrightarrow3x-1-3x^2+x+9x^2-3x+9x-3=2x^2+2x+3x+3\)
\(\Leftrightarrow6x^2+10x-4=2x^2+5x+3\)
\(\Leftrightarrow\left(6x^2-2x^2\right)+\left(10x-5x\right)=7\)
\(\Leftrightarrow4x^2+5x-7=0\)
\(\Leftrightarrow\left(2x\right)^2+4x.\frac{5}{4}+\frac{16}{25}+\frac{191}{25}=0\)
\(\Leftrightarrow\left(2x+\frac{5}{4}\right)^2-\frac{191}{25}=0\)
\(\left(2x+\frac{5}{4}\right)^2>0\)
\(\Rightarrow\left(2x+\frac{5}{4}\right)^2+\frac{191}{25}>0\)
=> PT vô nghiệm
\(4.\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
\(\Leftrightarrow\frac{\left(1-6x\right)\left(x+2\right)}{x^2-4}+\frac{\left(9x+4\right)\left(x-2\right)}{x^2-4}=\frac{2\left(3x-2\right)+1}{x^2-4}\)
\(\Rightarrow\left(1-6x\right)\left(x+2\right)+\left(9x+4\right)\left(x-2\right)=3\left(3x-2\right)+1\)
\(\Leftrightarrow x+2-6x^2-12x+9x^2-18x+4x-8=3x^2-2x+1\)
\(\Leftrightarrow3x^2-25x-6=3x^2-2x+1\)
\(\Leftrightarrow\left(3x^2-3x^2\right)+\left(-25x+2x\right)+\left(-6-1\right)=0\)
\(\Leftrightarrow-23x-7=0\)
\(\Leftrightarrow-23x=7\)
\(\Leftrightarrow x=\frac{-7}{23}\)
\(5.\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
\(\Leftrightarrow\frac{\left(3x+2\right)^2}{9x^2-4}-\frac{6\left(3x-2\right)}{9x^2-4}=\frac{9x^2}{9x^2-4}\)
\(\Rightarrow\left(3x+2\right)^2-6\left(3x-2\right)=9x^2\)
\(\Leftrightarrow9x^2+12x+4-18x+12=9x^2\)
\(\Leftrightarrow\left(9x^2-9x^2\right)+\left(12x-18x\right)+\left(4+12\right)=0\)
\(\Leftrightarrow-6x+16=0\)
\(\Leftrightarrow-6x=-16\)
\(\Leftrightarrow x=\frac{16}{6}\)
\(6.1+\frac{1}{x+2}=\frac{12}{8-x^3}\)
\(\Leftrightarrow\frac{\left(x+2\right)\left(8-x^3\right)}{\left(x+2\right)\left(8-x^3\right)}+\frac{1\left(8-x^3\right)}{\left(x+2\right)\left(8-x^3\right)}=\frac{12\left(x+2\right)}{\left(x+2\right)\left(8-x^3\right)}\)
\(\Rightarrow\left(x+2\right)\left(8-x^3\right)+1\left(8-x^3\right)=12\left(x+2\right)\)
\(\Leftrightarrow8x+x^4+16+2x^3+8-x^3=12x+24\)
\(\Leftrightarrow x^4+\left(2x^3-x^3\right)+\left(8x-12x\right)+\left(16-24\right)=0\)
\(\Leftrightarrow x^4+x^3-4x-8=0\)
\(\Leftrightarrow\left(x^4-4x\right)+\left(x^3-8\right)=0\)
Đến đấy mk tắc r xl bạn nhé
25 tháng 6 2019
ĐKXĐ: \(x\ne\pm2\)
\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
\(\Leftrightarrow\frac{\left(1-6x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(9x+4\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{x\left(3x-2\right)+1}{\left(x+2\right)\left(x-2\right)}\)
\(\Leftrightarrow x+2-6x^2-12x+9x^2-18x+4x-8=3x^2-2x+1\)
\(\Leftrightarrow-23x=7\)
\(\Leftrightarrow x=\frac{-7}{23}\left(tm\right)\)
Vậy: \(S=\left\{-\frac{7}{23}\right\}\)
=.= hk tốt!!
25 tháng 6 2019
Giải :
\(\text{ĐKXĐ}\: :\: x\ne\pm2\)
\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
\(\Leftrightarrow\frac{\left(1-6x\right)\left(x+2\right)+\left(9x+4\right)\left(x-2\right)}{x^2-4}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
Khử mẫu : \(\left(-6x^2-12x+x+2\right)+\left(9x^2-18x+4x-8\right)=3x^2-2x+1\)
\(\Leftrightarrow-23x=7\Leftrightarrow x=\frac{7}{23}\).
30 tháng 9 2019
\(\frac{2x-1}{3x^2+7x+2}+\frac{3}{9x^2+15x+4}-\frac{2x+7}{3x^2-5x-12}=\frac{5}{x+2}\)
\(\Leftrightarrow\frac{2x-1}{\left(3x+1\right)\left(x+2\right)}+\frac{3}{\left(3x+1\right)\left(3x+4\right)}-\frac{2x+7}{\left(4x+3\right)\left(x-3\right)}=\frac{5}{\left(x+2\right)}\)
\(\Leftrightarrow\frac{1}{x+2}-\frac{1}{3x+1}+\frac{1}{3x+1}-\frac{1}{3x+4}+\frac{1}{3x+4}-\frac{1}{x-3}=\frac{5}{x+2}\)
\(\Leftrightarrow\frac{1}{x+2}-\frac{1}{x-3}=\frac{5}{x+2}\)
\(\Leftrightarrow\frac{x-3-x-2}{\left(x+2\right)\left(x-3\right)}=\frac{5\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}\)
\(\Leftrightarrow5x-3=-5\)
\(\Leftrightarrow x=-\frac{2}{5}\)
Chúc bạn học tốt !!!
HS
2
SF
25 tháng 4 2020
\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\) (1)
đk: \(x\ne\pm\frac{2}{3}\)
(1)\(\Leftrightarrow\frac{\left(3x+2\right)^2-6\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}=\frac{9x^2}{9x^2-4}\)
\(\Leftrightarrow\frac{9x^2-6x+16}{\left(3x-2\right)\left(3x+2\right)}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Rightarrow9x^2-6x+16=9x^2\)
\(\Leftrightarrow16-6x=0\)
\(\Leftrightarrow x=\frac{8}{3}\)(thỏa mãn đkxđ)
vậy:...................
LT
25 tháng 4 2020
ĐKXĐ: \(x\ne\frac{2}{3};x\ne-\frac{2}{3}\)
\(\Leftrightarrow\frac{3x+2}{3x-2}-\frac{6}{3x+2}-\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}=0\)
\(\Leftrightarrow\frac{\left(3x+2\right)^2-6\left(3x-2\right)-9x^2}{\left(3x-2\right)\left(3x+2\right)}=0\)
\(\Leftrightarrow9x^2+12x+4-18x+12-9x^2=0\)
\(\Leftrightarrow16-6x=0\)
\(\Leftrightarrow6x=16\)
\(\Leftrightarrow x=\frac{8}{3}\left(TM\right)\)
Vậy \(S=\left\{\frac{8}{3}\right\}\)
HN
26 tháng 2 2019
a)\(-ĐKXĐ:\hept{\begin{cases}x-14\ne0;x-13\ne0\\x-9\ne0\\x-11\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne14;x\ne13\\x\ne9\\x\ne11\end{cases}}\)
- Ta có : \(\frac{2}{x-14}-\frac{5}{x-13}=\frac{2}{x-9}-\frac{5}{x-11}\)
\(\Leftrightarrow\frac{2}{x-14}-\frac{5}{x-13}-\frac{2}{x-9}+\frac{5}{x-11}=0\)
\(\Leftrightarrow\left(\frac{2}{x-14}-\frac{2}{x-9}\right)-\left(\frac{5}{x-13}-\frac{5}{x-11}\right)=0\)
\(\Leftrightarrow2\left(\frac{1}{x-14}-\frac{1}{x-9}\right)-5\left(\frac{1}{x-13}-\frac{1}{x-11}\right)=0\)\(\Leftrightarrow2.\frac{\left(x-9\right)-\left(x-14\right)}{\left(x-9\right)\left(x-14\right)}-5.\frac{\left(x-11\right)-\left(x-13\right)}{\left(x-11\right)\left(x-13\right)}=0\)
\(\Leftrightarrow2.\frac{5}{\left(x-9\right)\left(x-14\right)}-5.\frac{2}{\left(x-11\right)\left(x-13\right)}=0\)
\(\Leftrightarrow\frac{10}{\left(x-9\right)\left(x-14\right)}-\frac{10}{\left(x-11\right)\left(x-13\right)}=0\)
\(\Leftrightarrow10\left[\frac{1}{\left(x-9\right)\left(x-14\right)}-\frac{1}{\left(x-11\right)\left(x-13\right)}\right]=0\)
\(\Leftrightarrow\frac{\left(x-11\right)\left(x-13\right)}{\left(x-9\right)\left(x-14\right)\left(x-11\right)\left(x-13\right)}-\frac{\left(x-9\right)\left(x-14\right)}{\left(x-9\right)\left(x-14\right)\left(x-11\right)\left(x-13\right)}=\) \(0\)
\(\Leftrightarrow\left(x-11\right)\left(x-13\right)-\left(x-9\right)\left(x-14\right)=0\)
\(\Leftrightarrow x^2-24x+143-x^2+23x-126=0\)
\(\Leftrightarrow-x+17=0\Leftrightarrow-x=-17\Leftrightarrow x=17\)
Vậy pt có tập nghiệm S = { 17 }
P/s: Mk làm hơi lòng vòng, bn thông cảm nhé !
ĐKXĐ : x \(\ne\pm\frac{2}{3}\)
Khi đó \(\frac{3x-2}{3x-2}-\frac{2}{3x+2}=\frac{6x^2}{9x^2-4}\)
=> \(\frac{\left(3x-2\right)\left(3x+2\right)-2}{\left(3x-2\right)\left(3x+2\right)}=\frac{6x^2}{\left(3x-2\right)\left(3x+2\right)}\)
=> 9x2 - 6 = 6x2
=> 3x2 = 6
=> x2 = 2
=> x = \(\pm\sqrt{2}\)
Vậy tập nghiệm phương trình \(S=\left\{\pm\sqrt{2}\right\}\)
\(\frac{3x-2}{3x-2}-\frac{2}{3x+2}=\frac{6x^2}{9x^2-4}\)
\(\Leftrightarrow\frac{3x-2}{3x-2}-\frac{2}{3x+2}=\frac{6x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Leftrightarrow\frac{\left(3x-2\right)\left(3x+2\right)}{3x-2}-\frac{2\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}=\frac{6x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Leftrightarrow\frac{9x^2-4}{\left(3x-2\right)\left(3x+2\right)}-\frac{6x-4}{\left(3x+2\right)\left(3x-2\right)}=\frac{6x^2}{\left(3x+2\right)\left(3x-2\right)}\)
\(\Rightarrow9x^2-4-6x+4=6x^2\)
\(\Leftrightarrow9x^2-4-6x+4-6x^2=0\)
\(\Leftrightarrow3x^2-6x=0\)
\(\Leftrightarrow3x\left(x-2\right)0\)
\(\Leftrightarrow\orbr{\begin{cases}3x=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)