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T
30 tháng 4 2019
a,\(2x\left(x-3\right)=x-3.\)
\(\Leftrightarrow2x=1\)
\(\Leftrightarrow x=\frac{1}{2}\)
Vậy .....
b, \(\frac{x+2}{x-2}-\frac{5}{x}=\frac{8}{x^2-2x}\)
\(\Leftrightarrow\frac{\left(x+2\right)\cdot x}{\left(x-2\right)\cdot x}-\frac{5\left(x-2\right)}{x\left(x-2\right)}=\frac{8}{x^2-2x}\)
\(\Leftrightarrow\frac{x^2+2x-\left(5x-10\right)}{\left(x-2\right)x}=\frac{8}{x^2-2x}\)
\(\Leftrightarrow\frac{x^2+2x-5x+10}{x^2-2x}=\frac{8}{x^2-2x}\)
\(\Leftrightarrow x^2+2x-5x+10=8\)
\(\Leftrightarrow x^2-3x+10-8=0\)
\(\Leftrightarrow x^2-x-2x+2=0\)
\(\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)
Vậy ....
MT
7 tháng 3 2020
a) \(pt\Leftrightarrow\frac{6}{x^2+2}-1+\frac{7}{x^2+3}-1+\frac{12}{x^2+8}-1-\frac{3x^2+16}{x^2+10}+2=0\)
\(\Leftrightarrow\frac{4-x^2}{x^2+2}+\frac{4-x^2}{x^2+3}+\frac{4-x^2}{x^2+8}+\frac{4-x^2}{x^2+10}=0\)
\(\Leftrightarrow\left(4-x^2\right)\left(\frac{1}{x^2+2}+\frac{1}{x^2+3}+\frac{1}{x^2+8}+\frac{1}{x^2+10}\right)=0\)
\(\Leftrightarrow4-x^2=0\)(do \(\frac{1}{x^2+2}+\frac{1}{x^2+3}+\frac{1}{x^2+8}+\frac{1}{x^2+10}>0,\forall x\))
\(\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\)
\(KL...\)
7 tháng 3 2020
2x(8x - 1)2(4x - 1) = 9
<=> 512x4 - 256x3 + 40x2 - 2x = 9
<=> 512x4 - 256x3 + 40x2 - 2x - 9 = 0
<=> (2x - 1)(4x + 1)(64x4 - 16x + 9) = 0
vì 64x4 - 16x + 9 khác 0 nên:
<=> 2x - 1 = 0 hoặc 4x + 1 = 0
<=> x = 1/2 hoặc x = -1/4
23 tháng 4 2020
Bài 1:
a, \(\frac{1}{x+1}+\frac{2}{x-1}=\frac{1+x^2}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)
\(\Leftrightarrow\) \(\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{1+x^2}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow\) x - 1 + 2(x + 1) = 1 + x2
\(\Leftrightarrow\) x - 1 + 2x + 2 - 1 - x2 = 0
\(\Leftrightarrow\) -x2 + 3x = 0
\(\Leftrightarrow\) x(3 - x) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(TMĐKXĐ\right)\\x=3\left(TMĐKXĐ\right)\end{matrix}\right.\)
Vậy S = {0; 3}
b, \(\frac{x-2}{x+2}-\frac{x}{x-2}=\frac{8}{x^2-4}\) (ĐKXĐ: x \(\ne\) \(\pm\) 2)
\(\Leftrightarrow\) \(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{8}{\left(x+2\right)\left(x-2\right)}\)
\(\Rightarrow\) (x - 2)2 - x(x + 2) = 8
\(\Leftrightarrow\) (x - 2)2 - x(x + 2) - 8 = 0
\(\Leftrightarrow\) x2 - 4x + 4 - x2 - 2x - 8 = 0
\(\Leftrightarrow\) -6x - 4 = 0
\(\Leftrightarrow\) x = \(\frac{-2}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{-2}{3}\)}
c, \(\frac{1}{x}\) + \(\frac{2}{x-3}\) = \(\frac{1-5x}{x^2-3x}\) (ĐKXĐ: x \(\ne\) 0; x \(\ne\) 3)
\(\Leftrightarrow\) \(\frac{x-3}{x\left(x-3\right)}+\frac{2x}{x\left(x-3\right)}=\frac{1-5x}{x\left(x-3\right)}\)
\(\Rightarrow\) x - 3 + 2x = 1 - 5x
\(\Leftrightarrow\) 3x - 3 = 1 - 5x
\(\Leftrightarrow\) 3x + 5x = 1 + 3
\(\Leftrightarrow\) 8x = 4
\(\Leftrightarrow\) x = \(\frac{1}{2}\) (TMĐKXĐ)
Vậy S = {\(\frac{1}{2}\)}
Bài 2:
a, \(\frac{1}{x+2}=\frac{5}{2-x}+\frac{12+x}{x^2-4}\)
\(\Leftrightarrow\) \(\frac{1}{x+2}=\frac{-5}{x-2}+\frac{12+x}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\) \(\frac{x-2}{\left(x+2\right)\left(x-2\right)}=\frac{-5\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{12+x}{\left(x+2\right)\left(x-2\right)}\)
\(\Rightarrow\) x - 2 = -5(x + 2) + 12 + x
\(\Leftrightarrow\) x - 2 = -5x - 10 + 12 + x
\(\Leftrightarrow\) x - 2 = -4x + 2
\(\Leftrightarrow\) x + 4x = 2 + 2
\(\Leftrightarrow\) 5x = 4
\(\Leftrightarrow\) x = \(\frac{4}{5}\)
Vậy S = {\(\frac{4}{5}\)}
Chúc bn học tốt!! (Phần b hình như không có gì thì phải)
27 tháng 3 2020
a) \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{8}+\frac{2x-1}{12}\)
<=> \(\frac{x}{4}+\frac{5}{4}-\frac{2x}{3}+1=\frac{6x}{8}-\frac{1}{8}+\frac{2x}{12}-\frac{1}{12}\)
<=> \(-\frac{4}{3}x=-\frac{59}{24}\)
<=> \(x=\frac{59}{32}\)
Vậy S = { 59/32}
b) \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)
<=> \(\frac{x^2+14x+40}{12}-\frac{-x^2-2x+8}{4}=\frac{x^2+8x-20}{3}\)
<=> \(\left(\frac{x^2}{12}+\frac{x^2}{4}-\frac{x^2}{3}\right)+\left(\frac{14}{12}x+\frac{2}{4}x-\frac{8}{3}x\right)=-\frac{20}{8}+\frac{8}{4}-\frac{40}{12}\)
<=> \(-x=-8\)
<=> x = 8
Vậy S = { 8 }
1 tháng 6 2020
\(\frac{3x+2}{x+4}+\frac{2x+1}{x-2}=5-\frac{x-32}{x^2+2x-8}\)
\(\Leftrightarrow\) \(\frac{\left(3x+2\right)\left(x-2\right)}{\left(x+4\right)\left(x-2\right)}+\frac{\left(2x+1\right)\left(x+4\right)}{\left(x+4\right)\left(x-2\right)}=\frac{5\left(x+4\right)\left(x-2\right)}{\left(x+4\right)\left(x-2\right)}-\frac{x-32}{\left(x+4\right)\left(x-2\right)}\)
\(\Rightarrow\) (3x + 2)(x - 2) + (2x + 1)(x + 4) = 5(x + 4)(x - 2) - x + 32
\(\Leftrightarrow\) 3x2 - 6x + 2x - 4 + 2x2 + 8x + x + 4 = 5x2 - 10x + 20x - 40 - x + 32
\(\Leftrightarrow\) 5x2 + 5x = 5x2 + 9x - 8
\(\Leftrightarrow\) 5x2 + 5x - 5x2 - 9x + 8 = 0
\(\Leftrightarrow\) -4x + 8 = 0
\(\Leftrightarrow\) x - 2 = 0
\(\Leftrightarrow\) x = 2
Vậy S = {2}
\(\frac{x+2m}{x+3}+\frac{x-m}{x-3}=\frac{mx\left(x+1\right)}{x^2-9}\) (đkxđ: x \(\ne\) \(\pm\) 3)
\(\Leftrightarrow\) \(\frac{\left(x+2m\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{\left(x-m\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{mx\left(x+1\right)}{\left(x+3\right)\left(x-3\right)}\)
\(\Rightarrow\) (x + 2m)(x - 3) + (x - m)(x + 3) = mx(x + 1)
\(\Leftrightarrow\) x2 - 3x + 2mx - 6m + x2 + 3x - mx - 3m - mx2 - mx = 0
\(\Leftrightarrow\) (2 - m)x2 - 9m = 0
Thay m = 1 ta được:
(2 - 1)x2 - 9 . 1 = 0
\(\Leftrightarrow\) x2 - 9 = 0
\(\Leftrightarrow\) (x - 3)(x + 3) = 0
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(KTM\right)\\x=-3\left(KTM\right)\end{matrix}\right.\)
Vậy S = \(\varnothing\)
Thay m = 2 ta được:
(2 - 2)x2 - 9 . 2 = 0
\(\Leftrightarrow\) -18 = 0
\(\Rightarrow\) Pt vô nghiệm
Vậy S = \(\varnothing\)
Chúc bn học tốt!!
CQ
1
SF
25 tháng 4 2020
\(\frac{1}{x+2}=\frac{5}{2-x}+\frac{12+x}{x^2-4}\) (1)
đkxđ: \(x\ne\pm2\)
(1)\(\Leftrightarrow\frac{\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{-5\left(x+2\right)+12+x}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow x-2=-5\left(x+2\right)+12+x\)
\(\Leftrightarrow5x=4\)
\(\Leftrightarrow x=\frac{5}{4}\)(thỏa mãn đkxđ)