a)
\(\dfrac{x-3}{5}+\dfrac{1+2x}{3}=6\\ < =>3x-9+5+10x=90\)
`<=> 13x-4=90`
`<=>13x=94`
`<=>x=94/13`
b)
`(2x-3)(x^2 +1)=0`
\(< =>\left[{}\begin{matrix}2x-3=0\\x^2+1=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{3}{2}\\x^2=-1\left(voli\right)\end{matrix}\right.\\ < =>x=\dfrac{3}{2}\)
c)
\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\left(x\ne-1;x\ne2\right)\\ < =>\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)
suy ra
`<=>2x-4-x-1=3x-11`
`<=>2x-x-3x=-11+4+1`
`<=>-2x=-6`
`<=>x=3(tm)`
a) \(\dfrac{x-3}{5}+\dfrac{1+2x}{3}=6\)
\(\Leftrightarrow\dfrac{3.\left(x-3\right)}{15}+\dfrac{5.\left(1+2x\right)}{15}=\dfrac{90}{15}\)
\(\Rightarrow3x-9+5+10x=90\)
\(\Leftrightarrow13x=94\)
\(\Leftrightarrow x=\dfrac{94}{13}\)
b) \(\left(2x-3\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\x^2-1=0\end{matrix}\right.\)
* \(2x-3=0\Leftrightarrow x=\dfrac{3}{2}\)
* \(x^2-1=0\Leftrightarrow x^2=-1\) ( vô lí )
c) \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\) ĐKXĐ: \(x\ne-1;x\ne2\)
\(\Leftrightarrow\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{x+1}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)
\(\Rightarrow2x-4-x-1=3x-11\)
\(\Leftrightarrow-2x=-6\)
\(\Leftrightarrow x=3\) ( nhận )
Bạn tụ kết luận nghiệm nha.
