\(\frac{x^2+x+1}{x+1}+\frac{x^2+2x+2}{x+2}+\frac{x^2+3x+3}{x+3}+\frac{x^2+4x+4}{x+4}=0\)
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Bµi 5: Gi¶i PT sau.
a,frac{5x-2}{2-2x}+frac{2x-1}{2}+frac{x^2+x-3}{1-x}1
b,frac{6x-1}{2-x}+frac{9x+4}{x+2}frac{3x^2-2x+1}{x^2-4}
c,frac{1}{x-1}+frac{2x^2-5}{x^3-1}frac{4}{x^2+x+1}
d) (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 0
e) x4 + 2x3 + 4x2 + 2x + 1 0
f,frac{3x-1}{x-1}-frac{2x+5}{x+3}+frac{4}{x^2+2x-3}1
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Bµi 5: Gi¶i PT sau.
\(a,\frac{5x-2}{2-2x}+\frac{2x-1}{2}+\frac{x^2+x-3}{1-x}=1\)
b,\(\frac{6x-1}{2-x}+\frac{9x+4}{x+2}=\frac{3x^2-2x+1}{x^2-4}\)
\(c,\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
d) (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 = 0
e) x4 + 2x3 + 4x2 + 2x + 1 = 0
\(f,\frac{3x-1}{x-1}-\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}=1\)
a) \(\frac{5x-2}{2-2x}+\frac{2x-1}{2}+\frac{x^2+x-3}{1-x}=1\)
ĐK: x≠1
<=>\(\frac{5x-2}{2\left(1-x\right)}+\frac{2x-1}{2}\frac{x^2+x-3}{1-x}=1\)
<=>\(\frac{5x-2+\left(1-x\right).\left(2x-1\right)+2\left(x^2+x-3\right)}{2\left(1-x\right)}=1\)
<=>\(\frac{5x-2+2x-1-2x^2+x+2x^2+2x-6}{2\left(1-x\right)}=1\)
<=>\(\frac{10x-9}{2\left(1-x\right)}=1\)
<=> 10x-9=2(1-x)
<=>10x-9=2-2x
<=> 10x+2x= 2+9
<=> 12x=11
<=> x= \(\frac{11}{12}\left(tm\right)\)
b) \(\frac{6x-1}{2-x}+\frac{9x+4}{x+2}=\frac{3x^2-2x+1}{x^2-4}\)
ĐK: x≠2, x≠-2
<=>\(\frac{6x-1}{-\left(x-2\right)}+\frac{9x+4}{x+2}-\frac{3x^2-2x+1}{\left(x-2\right)\left(x+2\right)}=0\)
<=> -(x+2).(6x-1)+(x-2).(9x+4)-(3x2-2x+1)=0
<=> -(6x2-x+12x-2)+9x2+4x-18x-8-3x2+2x-1 = 0
<=> -6x2-11x+2+9x2+4x-18x-8-3x2+2x-1=0
<=> -23x-7=0
<=> -23x=7
<=> x= \(\frac{-7}{23}\left(tm\right)\)
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tham khảo câu d trong
https://hoc24.vn/hoi-dap/question/919967.html
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c) \(\frac{1}{x-1}\)+\(\frac{2x^2-5}{x^3-1}\)=\(\frac{4}{x^2+x+1}\) (ĐKXĐ:x≠1)
⇔\(\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\)+\(\frac{2x^2-5}{\left(x-1\right)\left(x^2+x+1\right)}\)=\(\frac{4\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
⇒x2+x+1+2x2-5=4x-4
⇔3x2-3x=0
⇔3x(x-1)=0
⇔x=0 (TMĐK) hoặc x=1 (loại)
Vậy tập nghiệm của phương trình đã cho là:S={0}
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Giải các phương trình sau:
a) frac{4}{x-1}-frac{5}{x-2}-3
b) 3x-frac{1}{x-2}frac{x-1}{2-x}
c) frac{x+4}{x^2-3x+2}+frac{x+1}{x^2-4x+3}frac{2x+5}{x^2-4x+3}
d) frac{2}{x^2-4}-frac{1}{xleft(x-2right)}+frac{x-4}{xleft(x+2right)}0
e) frac{4x}{x^2+4x+3}-16left(frac{1}{x+3}-frac{1}{2x-2}right)
f) frac{3}{4xleft(x-5right)}+frac{15}{50-2x^2}frac{7}{6x+30}
g) frac{1}{x-1}+frac{2x^2-5}{x^3-1}frac{4}{x^2+x+1}
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Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x-2}\right)\)
f) \(\frac{3}{4x\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)
g) \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
\(\frac{x^2+x+1}{x+1}+\frac{x^2+2x+2}{x+2}+\frac{x^2+3x+3}{x+3}+\frac{x^2+4x+4}{x+4}=0\)
Giải các phương trình sau:
a) frac{4}{x-1}-frac{5}{x-2}-3
b) 3x-frac{1}{x-2}frac{x-1}{2-x}
c) frac{x+4}{x^2-3x+2}+frac{x+1}{x^2-4x+3}frac{2x+5}{x^2-4x+3}
d) frac{2}{x^2-4}-frac{1}{xleft(x-2right)}+frac{x-4}{xleft(x+2right)}0
e) frac{4x}{x^2+4x+3}-16left(frac{1}{x+3}-frac{1}{2x+2}right)
f) frac{3}{4left(x-5right)}+frac{15}{50-2x^2}frac{7}{6x+30}
g) frac{1}{x-1}+frac{2x^2-5}{x^3-1}frac{4}{x^2+x+1}
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Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)
f) \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)
g) \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
Giải các phương trình sau:
a) frac{4}{x-1}-frac{5}{x-2}-3
b) frac{x+4}{x^2-3x+2}+frac{x+1}{x^2-4x+3}frac{2x+5}{x^2-4x+3}
c) 3x-frac{1}{x-2}frac{x-1}{2-x}
d) frac{2}{x^2-4}-frac{1}{xleft(x-2right)}+frac{x-4}{xleft(x+2right)}0
e) frac{4x}{x^2+4x+3}-16left(frac{1}{x+3}-frac{1}{2x+2}right)
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Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
c) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)
giải ác phương trình sau:
1)frac{x+2}{2x-4}-frac{4x}{x^2-4}0
2)frac{x}{x-1}-frac{5x-3}{x^2-1}0
3)frac{1}{x-3}-frac{4}{x+3}frac{3x}{9-x^2}
4)frac{1}{2x-3}-frac{3}{xleft(2x-3right)}frac{5}{x}
5)frac{-3}{2x}-frac{x+1}{x+2}frac{-3}{xleft(x+2right)}
6)frac{x+2}{x-2}-frac{1}{x}frac{2}{x^2-2x}
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giải ác phương trình sau:
1)\(\frac{x+2}{2x-4}-\frac{4x}{x^2-4}=0\)
2)\(\frac{x}{x-1}-\frac{5x-3}{x^2-1}=0\)
3)\(\frac{1}{x-3}-\frac{4}{x+3}=\frac{3x}{9-x^2}\)
4)\(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
5)\(\frac{-3}{2x}-\frac{x+1}{x+2}=\frac{-3}{x\left(x+2\right)}\)
6)\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\)
1, Đk x≠2;-2
\(\frac{x+2}{2x-4}-\frac{4x}{x^2-4}=0\\ =>\frac{x+2}{2\left(x-2\right)}-\frac{4x}{\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{\left(x+2\right)^2}{2\left(x^2-4\right)}-\frac{8x}{2\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{x^2+4x+4-8x}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x^2-4x+4}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x-2}{2\left(x+2\right)}=0\\ =>x-2=0\\ =>x=2\left(loại\right)\)
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TÌM X BIẾT \(\frac{X-1}{X^2-9X+20}+\frac{2X-2}{X^2-6X+8}+\frac{3X-3}{X^2-X-2}+\frac{4X-4}{X^2+6X+5}=0\)
\(\frac{x-1}{x^2-9x+20}+\frac{2x-2}{x^2-6x+8}+\frac{3x-3}{x^2-x-2}+\frac{4x-4}{x^2+6x+5}=0\)
\(\Leftrightarrow\frac{x-1}{\left(x-5\right)\left(x-4\right)}+\frac{2\left(x-1\right)}{\left(x-4\right)\left(x-2\right)}+\frac{3\left(x-1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{4\left(x-1\right)}{\left(x+1\right)\left(x+5\right)}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\frac{10}{x^2-25}\right)=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
PS: Điều kiện xác đinh bạn tự làm nhé
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Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x-2\right)}=0\)
Giải các phương trình sau:
a) frac{4}{x-1}-frac{5}{x-2}-3
b) 3x-frac{1}{x-2}frac{x-1}{2-x}
c) frac{x+4}{x^2-3x+2}+frac{x+1}{x^2-4x+3}frac{2x+5}{x^2-4x+3}
d) frac{2}{x^2-4}-frac{1}{xleft(x-2right)}+frac{x-4}{xleft(x+2right)}0
e) frac{4x}{x^2+4x+3}-16left(frac{1}{x+3}-frac{1}{2x+2}right)
f) frac{3}{4left(x-5right)}+frac{15}{50-2x^2}frac{7}{6x+30}
g)frac{1}{x-1}+frac{2x^2-5}{x^3-1}frac{4}{x^2+x+1}
h) frac{12x+1}{6x-2}-frac{9x-5}{3x+1}frac{108x-36x^2-9}{4left(9x^2-1right)}
i) x+frac{1}{x}x^...
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Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)
f) \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)
g)\(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
h) \(\frac{12x+1}{6x-2}-\frac{9x-5}{3x+1}=\frac{108x-36x^2-9}{4\left(9x^2-1\right)}\)
i) \(x+\frac{1}{x}=x^2+\frac{1}{x^2}\)
j) \(\frac{1}{x}+2=\left(\frac{1}{x}+2\right)\left(x^2+2\right)\)
k) \(\left(x+1+\frac{1}{x}\right)^2=\left(x-1-\frac{1}{x}\right)^2\)