Question

Answer 1

a/

\(\Leftrightarrow15x+10-4x-1=0\)

\(\Leftrightarrow11x-9=0\Rightarrow x=\dfrac{9}{11}\)

b/

\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)

c/

đk : x khác -1 ; khác 2 

\(\Leftrightarrow\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{x+1}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{2x-4}{...}-\dfrac{x+1}{...}-\dfrac{3x-11}{....}=0\)

<=> 2x-4-x-1-3x+11=0

<=> 6-2x=0

=> x = 3 (tm)

 

Answer 2

a) \(5\left(3x+2\right)=4x+1\\ \Leftrightarrow15x+10=4x+1\\ \Leftrightarrow15x-4x=-10+1\\ \Leftrightarrow11x=-9\\ \Leftrightarrow x=\dfrac{-9}{11}\)

Vậy \(x=\dfrac{-9}{11}\) là nghiệm của phương trình

b) \(\left(x-3\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)

Vậy \(x\in\left\{3;-4\right\}\) là nghiệm của phương trình

c) \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\left(ĐK:x\ne-1;x\ne2\right)\\ \Leftrightarrow\dfrac{2\left(x-2\right)-\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Rightarrow2x-4-x-1=3x-11\\ \Leftrightarrow2x-x-3x=-11+4+1\\ \Leftrightarrow-2x=-6\\ \Leftrightarrow x=3\left(tmđk\right)\)

Vậy x = 3 là nghiệm của phương trình

Answer 3

a.\(5\left(3x+2\right)=4x+1\)

\(\Leftrightarrow15x+10=4x+1\)

\(\Leftrightarrow11x=-9\)

\(\Leftrightarrow x=-\dfrac{9}{11}\)

b.\(\left(x-3\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)

c.\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

\(ĐK:x\ne-1;2\)

\(\Leftrightarrow\dfrac{2\left(x-2\right)-\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

\(\Leftrightarrow2\left(x-2\right)-\left(x+1\right)=3x-11\)

\(\Leftrightarrow2x-4-x-1-3x+11=0\)

\(\Leftrightarrow-6x+6=0\)

\(\Leftrightarrow-6x=-6\)

\(\Leftrightarrow x=1\left(tm\right)\)