\(\frac{2}{x^2-4}-\frac{x-1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\) \(\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-2x-3}\)giải dùm minh nhá
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TL:
a)
\(\frac{14\left(x-3\right)}{21}+\frac{7\left(x-5\right)}{21}=\frac{13x+4}{21}\)
\(\frac{14x-42+7x-35}{21}=\frac{13x+4}{21}\)
21x-77=13x+4
21x-13x=77+4
8x=81
x=\(\frac{81}{8}\)
2 câu còn lại bn lm cách tương tự
hc tốt
1.
\(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)
\(MC:12\)
Quy đồng :
\(\Rightarrow\frac{3.\left(2x+3\right)}{12}-\left(\frac{2.\left(5x+3\right)}{12}\right)=\frac{3x-4}{12}\)
\(\frac{6x+9}{12}-\left(\frac{10x+6}{12}\right)=\frac{3x-4}{12}\)
\(\Leftrightarrow6x+9-\left(10x+6\right)=3x-4\)
\(\Leftrightarrow6x+9-3x=-4-9+16\)
\(\Leftrightarrow-7x=3\)
\(\Leftrightarrow x=\frac{-3}{7}\)
2.\(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)
\(MC:20\)
Quy đồng :
\(\frac{15.\left(2x+1\right)}{20}-\frac{20}{20}=\frac{2.\left(15x-1\right)}{20}\)
\(\Leftrightarrow15\left(2x+1\right)-20=2\left(15x-1\right)\)
\(\Leftrightarrow30x+15-20=15x-2\)
\(\Leftrightarrow15x=3\)
\(\Leftrightarrow x=\frac{3}{15}=\frac{1}{5}\)
1. \(\frac{x-1}{2}-\frac{x+1}{15}-\frac{2x-13}{6}=0\)
\(\Leftrightarrow\frac{x-1}{2}.30-\frac{x+1}{15}.30-\frac{2x-13}{6}.30=0.30\)
\(\Leftrightarrow15\left(x-1\right)-2\left(x+1\right)-5\left(2x-13\right)=0\)
\(\Leftrightarrow3x+48=0\)
\(\Leftrightarrow3x=0-48\)
\(\Leftrightarrow3x=-48\)
\(\Leftrightarrow x=\frac{-48}{3}=-16\)
=> x = -16
a/ \(\Leftrightarrow\left(x+2\right)^2-3\left|x+2\right|=0\)
\(\Leftrightarrow\left|x+2\right|^2-3\left|x+2\right|=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x+2\right|=0\\\left|x+2\right|=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-2\\x+2=3\\x+2=-3\end{matrix}\right.\)
b/
\(\Leftrightarrow\left|x+2\right|^2-3\left|x+2\right|-4=0\)
\(\Leftrightarrow\left(\left|x+2\right|+1\right)\left(\left|x+2\right|-4\right)=0\)
\(\Leftrightarrow\left|x+2\right|-4=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=4\\x+2=-4\end{matrix}\right.\)
c/
\(\Leftrightarrow\left|x^2-3\right|^2-6\left|x^2-3\right|+5=0\)
\(\Leftrightarrow\left(\left|x^2-3\right|-1\right)\left(\left|x^2-3\right|-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x^2-3\right|=1\\\left|x^2-3\right|=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-3=1\\x^2-3=-1\\x^2-3=5\\x^2-3=-5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2=4\\x^2=2\\x^2=8\\x^2=-2\left(l\right)\end{matrix}\right.\)
d/ ĐKXĐ: ...
\(\Leftrightarrow\frac{\left|x-2\right|^2}{\left(x-1\right)^2}+\frac{2\left|x-4\right|}{x-1}=3\)
Đặt \(\frac{\left|x-2\right|}{x-1}=a\)
\(a^2+2a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left|x-2\right|=x-1\\\left|x-2\right|=-3\left(x-1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-2\right|=x-1\left(x\ge1\right)\\\left|x-2\right|=3-3x\left(x\le1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=x-1\left(vn\right)\\x-2=1-x\\x-2=3-3x\\x-2=3x-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{3}{2}\\x=\frac{4}{5}\\x=\frac{1}{2}\end{matrix}\right.\)
e/ ĐKXĐ: ...
Đặt \(\left|\frac{2x-1}{x+2}\right|=a>0\)
\(a-\frac{2}{a}=1\Leftrightarrow a^2-a-2=0\)
\(\Rightarrow\left[{}\begin{matrix}a=-1\left(l\right)\\a=2\end{matrix}\right.\) \(\Rightarrow\left|\frac{2x-1}{x+2}\right|=2\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=2\left(x+2\right)\\2x-1=-2\left(x+2\right)\end{matrix}\right.\)
Giải phương trình
a) \(\frac{2x}{x-1}-\frac{x}{x-2}=\frac{x^2}{\left(x-1\right)\left(x-2\right)}\left(x\ne1,x\ne2\right)\)
\(\Leftrightarrow\frac{2x\left(x-2\right)-x\left(x-1\right)-x^2}{\left(x-1\right)\left(x-2\right)}=0\)
\(\Rightarrow2x^2-x^2-x^2-4x+x=0\)
\(\Leftrightarrow-3x=0\Leftrightarrow x=0\left(tm\right)\)
KL: Vậy...
b)\(\frac{1}{x+2}-\frac{6}{x-1}+\frac{8}{\left(x+2\right)\left(x-1\right)}=0\left(x\ne-2,x\ne1\right)\)
\(\Leftrightarrow\frac{\left(x-1\right)-6\left(x+2\right)+8}{\left(x+2\right)\left(x-1\right)}=0\)
\(\Rightarrow x-1-6x-12+8=0\)
\(\Leftrightarrow-5x=-7\Leftrightarrow x=\frac{7}{5}\left(tm\right)\)
c) \(\frac{x+2}{x+3}-\frac{x+1}{x-1}=\frac{4}{\left(x+3\right)\left(x-1\right)}\left(x\ne-3,x\ne1\right)\)
\(\Leftrightarrow\frac{\left(x+2\right)\left(x-1\right)-\left(x+1\right)\left(x+3\right)-4}{\left(x+3\right)\left(x-1\right)}=0\)
\(\Rightarrow x^2+x-2-x^2-4x-3-4=0\)
\(\Leftrightarrow-3x=9\Leftrightarrow x=-3\left(ktm\right)\)
Câu 1 :
- Gọi chiều dài miếng đất là x ( m, x > 6 )
=> Chiều rộng miếng đất là : x - 6 ( m )
=> Chu vi miếng đất đó là : \(2\left(x+x-6\right)\) ( m )
Theo đề bài chu vi mảnh đất đó là 60m nên ta có phương trình :
\(2\left(x+x-6\right)=60\)
=> \(2x-6=30\)
=> \(2x=24\)
=> \(x=12\) ( TM )
Mà diện tích mảnh đất là : \(x\left(x-6\right)\)
=> Smảnh đất = \(12\left(12-6\right)=12.6=72\left(m^2\right)\)
\(\frac{2}{x^2-4}-\frac{x-1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)Đk \(x\ne\pm2;x\ne0\)
\(\Rightarrow\frac{2}{\left(x-2\right)\left(x+2\right)}-\frac{x-1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
\(\Rightarrow\frac{2x-\left(x-1\right)\left(x+2\right)+\left(x-4\right)\left(x-2\right)}{x\left(x-2\right)\left(x+2\right)}=0\)
\(\Rightarrow2x-\left(x-1\right)\left(x+2\right)+\left(x-4\right)\left(x-2\right)=0\)
\(\Rightarrow2x-x^2-x+2+x^2-6x+8=0\)
\(\Rightarrow-5x+10=0\)
\(\Rightarrow-5x=-10\)
\(\Rightarrow x=2\)Loại
Ko có gt x thỏa mãn
\(\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-2x-3}\)
\(\Rightarrow\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-3x+x-3}\)
\(\Rightarrow\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}\)Đk \(x\ne3;x\ne-1\)
\(\Leftrightarrow\frac{1}{3-x}-\frac{1}{x+1}-\frac{x}{x-3}-\frac{\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}=0\)
\(\Rightarrow-\frac{1}{x-3}-\frac{1}{x+1}-\frac{x}{x-3}+\frac{\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}=0\)
\(\Rightarrow\frac{-1\left(x+1\right)-1\left(x-3\right)-x\left(x+1\right)+\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}=0\)
\(\Rightarrow-\left(x+1\right)-\left(x-3\right)-x\left(x+1\right)+\left(x-1\right)^2=0\)
\(\Rightarrow x-1-x+3-x^2-x+x^2-2x+1=0\)
\(\Rightarrow-3x+3=0\)
\(\Rightarrow-3x=-3\)
\(\Rightarrow x=1\)