Giai phương trình sau:
\(\frac{3x-3}{x^2-1}=\frac{x}{x-2}-1\)
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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
HM
1
AH
Akai Haruma
Giáo viên
5 tháng 5 2020
Lời giải:
a) $x^2-x=0$
$\Leftrightarrow x(x-1)=0\Rightarrow x=0$ hoặc $x-1=0$
hay $x=0$ hoặc $x=1$
Vậy tập nghiệm của pt là $S=\left\{0;1\right\}$
b)
ĐKXĐ: $x\neq -3$
PT $\Leftrightarrow \frac{3x+2-(3x+1)}{x+3}=1$
$\Leftrightarrow \frac{1}{x+3}=1$
$\Rightarrow x+3=1\Rightarrow x=-2$ (thỏa mãn)
Vậy PT có nghiệm duy nhất $x=-2$
LM
2 tháng 3 2019
Cho x,y,z là các sô dương.Chứng minh rằng x/2x+y+z+y/2y+z+x+z/2z+x+y<=3/4
13 tháng 1 2016
khó quá mk mới học lớp 6 nên k giải đc thông cảm cho mk nha
\(\frac{3x-3}{x^2-1}=\frac{x}{x-2}-1\)ĐKXĐ : \(x\ne\pm1;x\ne2\)
\(\Leftrightarrow\frac{3\left(x-1\right)\left(x-2\right)}{\left(x-1\right)\left(x+1\right)\left(x-2\right)}=\frac{x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{\left(x+1\right)\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow\frac{3\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}=\frac{x\left(x+1\right)-\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}\)
\(\Rightarrow3x-6=x^2+x-x^2+x+2\)
\(\Leftrightarrow3x-6-2x-2=0\)
\(\Leftrightarrow x-8=0\)
\(\Leftrightarrow x=8\)( thỏa )
Vậy....
\(\frac{3x-3}{x^2-1}=\frac{x}{x-2}-\)\(1\)
\(\Leftrightarrow\) \(\frac{3.\left(x-1\right)}{\left(x-1\right).\left(x+1\right)}\)\(=\frac{x}{x-2}-1\)
\(\Leftrightarrow\)\(\frac{3}{x+1}=\frac{x}{x-2}-1\)
ĐKXĐ : \(x\ne-1,2\)
\(\Leftrightarrow\)\(\frac{3.\left(x-2\right)}{\left(x+1\right).\left(x-2\right)}\)\(=\frac{x.\left(x+1\right)}{\left(x+1\right).\left(x-2\right)}\)\(-\frac{\left(x+1\right).\left(x-2\right)}{\left(x+1\right).\left(x-2\right)}\)
\(\Leftrightarrow\)\(3x-6=x^2+x-\left(x^2-2x+x-2\right)\)
\(\Leftrightarrow\)\(3x-6=x^2+x-x^2+x+2\)
\(\Leftrightarrow\)\(3x-x-x=6+2\)
\(\Leftrightarrow\) \(x=8\)
Vậy phương trình có nghiệm là : \(x=8\)