`2x-3=3(x-1) +x+2`
`<=> 2x-3 = 3x-3 +x+2`
`<=>2x-3-3x+3-x-2=0`
`<=> -2x-2=0`
`<=> -2x=2`
`<=> x= -1`
Vậy phương trình có nghiệm `x=-1`
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`2x(x-3)-5(x-3)=0`
`<=>(x-3)(2x-5)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\2x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{5}{2}\end{matrix}\right.\)
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\(\dfrac{2x}{x+1}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\)
\(ĐKXĐ:\left\{{}\begin{matrix}x+1\ne0\\x-4\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\x\ne4\end{matrix}\right.\)
Ta có : \(\dfrac{2x}{x+1}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\)
\(\Leftrightarrow\dfrac{2x\left(x-4\right)}{\left(x+1\right)\left(x-4\right)}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\)
`=> 2x^2 - 8x -x^2 +x-8=0`
`<=> x^2 -7x -8=0`
`<=> x^2 +x-8x-8=0`
`<=> x(x+1) - 8(x+1)=0`
`<=>(x+1)(x-8)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\left(l\right)\\x=8\end{matrix}\right.\)
Vậy pt có nghiệm `x=8`
2:
a: =>2x-3=3x-3+x+2
=>4x-1=2x-3
=>2x=-2
=>x=-1
b: =>(x-3)(2x-5)=0
=>x=5/2 hoặc x=3
c: =>2x(x-4)=x^2-x+8
=>2x^2-8x-x^2+x-8=0
=>x^2-7x-8=0
=>(x-8)(x+1)=0
=>x=8(nhận) hoặc x=-1(loại)
Câu 2 :
a. \(2x-3=3\left(x-1\right)+x+2\\ \Leftrightarrow2x-3=3x-3+x+2\\ \Leftrightarrow2x-3x-x=3-3+2\\ \Leftrightarrow-2x=2\\ \Leftrightarrow x=-1\)
b. \(2x\left(x-3\right)-5\left(x-3\right)=0\\ \Leftrightarrow\left(2x-5\right)\left(x-3\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\x-3=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\x=3\end{matrix}\right.\)
c. \(\dfrac{2x}{x+1}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\\ \Leftrightarrow\dfrac{2x\left(x-4\right)}{\left(x+1\right)\left(x-4\right)}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\\ \Leftrightarrow\dfrac{2x^2-8x}{\left(x+1\right)\left(x-4\right)}=\dfrac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\\ \Leftrightarrow2x^2-8x-x^2+x=8\\ \Leftrightarrow x^2-7x=8\\ \Leftrightarrow x\left(x-7\right)=8\\ \Leftrightarrow\left\{{}\begin{matrix}x=8\\x=15\end{matrix}\right.\)
