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a, \(\frac{1-x}{x+1}+3=\frac{2x+3}{x+1}\)
\(=>\frac{1-x+x+1}{x+1}+2=\frac{1}{x+1}+2\)
\(=>\frac{2}{x+1}=\frac{1}{x+1}\)
\(=>2x+2=x+1\)
\(=>2x-x=1-2=-1\)
\(=>x=-1\)
vậy nghiệm của phương trình trên là {-1}
À quên ĐKXĐ của câu a là \(x\ne-1\)
Nên \(x\in\varnothing\)nhé :v
\(\left(x-1\right)\left(x+1\right)-2\left(2x+3\right)\le\left(x-2\right)^2+x\)
\(\Leftrightarrow x^2-1-4x-6\le x^2-4x+4+x\)
\(\Leftrightarrow x^2-4x-7\le x^2-3x+4\)
\(\Leftrightarrow x^2-4x-x^2+3x\le7+4\)
\(\Leftrightarrow-x\le11\)
\(\Leftrightarrow x\le-11\)
Bài 1"
a) \(x^2-4x+3\ge0\)
\(\Leftrightarrow x^2-x-3x+3\ge0\)
\(\Leftrightarrow x\left(x-1\right)-3\left(x-1\right)\ge0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)\ge0\)
\(\Leftrightarrow\begin{cases}x-1\ge0\\x-3\ge0\end{cases}\) hoặc \(\begin{cases}x-1\le0\\x-3\le0\end{cases}\)
\(\Leftrightarrow\begin{cases}x\ge1\\x\ge3\end{cases}\) hoặc \(\begin{cases}x\le1\\x\le3\end{cases}\)
\(\Leftrightarrow x\ge3\) hoặc \(x\le1\)
\(a,\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\)
\(\Leftrightarrow\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x-1\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{2\left(x^2+2\right)}{\left(x+2\right)\left(x-2\right)}\)
=> ( x + 1)( x + 2) + ( x - 1)( x - 2) = 2x2 + 4
<=> x2 + 2x + x + 2 + x2 - 2x - x + 2 = 2x2 + 4
<=> x2 + 2x + x + x2 - 2x - x - 2x2 = 4 - 2 - 2
<=> 0x = 0
Vậy phương trình vô số nghiệm
\(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)
\(< =>\frac{5x-131}{19}=\frac{1631-52x-\frac{38x-684}{5}}{209}\)
\(< =>\left(5x-131\right)209=\left(1631-52x-\frac{38x-684}{5}\right)19\)
\(< =>55x-1441=1631-52x-\frac{38x-684}{5}\)
\(< =>3072-107x=\frac{38x-684}{5}\)
\(< =>\left(3072-107x\right)5=38x-684\)
\(< =>15360-535x-38x-684=0\)
\(< =>14676=573x< =>x=\frac{14676}{573}=\frac{4892}{191}\)
nghệm xấu thế
\(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)
\(< =>\frac{8x+176}{45}-\frac{41x+817}{45}=\frac{11x+415}{45}\)
\(< =>993-33x-11x-415=0\)
\(< =>578=44x< =>x=\frac{289}{22}\)
a) \(\left(x-2\right)\left(x+1\right)=x^2-4\)
\(\Leftrightarrow x^2+x-2x-2=x^2-4\)
\(\Leftrightarrow x^2-x-2=x^2-4\)
\(\Leftrightarrow-x-2=-4\)
\(\Leftrightarrow-x=-4+2\)
\(\Leftrightarrow-x=-2\)
\(\Leftrightarrow x=2\)
Vậy: phương trình có tập nghiệm: S = {2}
a) \(\left(x-2\right)\left(x+1\right)=x^2-4\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=\left(x-2\right)\left(x+2\right)\)
\(\Leftrightarrow x+1=x+2\)
\(\Leftrightarrow x+1-x-2=0\)
\(\Leftrightarrow-1=0\left(vl\right)\)
Vậy pt vô no
b) \(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x+2\right)}\)
\(\frac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\frac{x+1}{\left(x+1\right)\left(x-2\right)}=\frac{3x-11}{\left(x+1\right)\left(x+2\right)}\)
\(\frac{2x-4-x-1}{\left(x+1\right)\left(x-2\right)}=\frac{3x-11}{\left(x+1\right)\left(x+2\right)}\)
\(\frac{-5}{\left(x+1\right)\left(x-2\right)}=\frac{3x-11}{\left(x+1\right)\left(x+2\right)}\)
\(\Leftrightarrow-5\left(x+2\right)=\left(3x-11\right)\left(x-2\right)\)
\(-5x+2=3x^2-11x-6x+22\)
\(3x^2-17x+22+5x-2=3x^2-12x+20=0\)
đến đây mk chịu ~