Bài làm
a) 3x - 1 = 2x + 4
<=> x = 5
Vậy x = 5 là nghiệm phương trình.
b) x( x + 3 ) = ( 2x + 1 )( x + 3 )
<=> x( x + 3 ) - ( 2x + 1 )( x + 3 ) = 0
<=> ( x + 3 )( x - 2x - 1 ) = 0
<=> ( x + 3 )( -x - 1 ) = 0
<=> x + 3 = 0 hoặc -x - 1 = 0
<=> x = -3 hoặc x = -1
Vậy x = -3 hoặc x = -1 là tập nghiệm phương trình
c) quy đồng mẫu ra r lm, bh ngủ.
Bài 1
a)\(3x-1=2x+4\)
\(\Leftrightarrow x=5\)
b) \(x\left(x+3\right)=\left(2x+1\right)\left(x+3\right)\)
\(x\left(x+3\right)-\left(2x+1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-2x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\x-2x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-3\\\left(x-1\right)^2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-3\\x=1\end{matrix}\right.\)
c) \(\frac{1}{x+1}+\frac{5}{x-2}=\frac{3x}{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow\frac{1\left(x-2\right)+5\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\frac{3x}{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow x-2+5x+5=3x\)
\(\Leftrightarrow3x=3\)
\(\Rightarrow x=1\)
Bài 1:
a, 3x - 1 = 2x + 4
\(\Leftrightarrow\) 3x - 2x = 4 + 1
\(\Leftrightarrow\) x = 5
Vậy S = {5}
b, x(x + 3) = (2x + 1)(x + 3)
\(\Leftrightarrow\) x(x + 3) - (2x + 1)(x + 3) = 0
\(\Leftrightarrow\) (x + 3)(-x - 1) = 0
\(\Leftrightarrow\) x + 3 = 0 hoặc -x - 1 = 0
\(\Leftrightarrow\) x = -3 và x = -1
Vậy S = {-3; -1}
c, \(\frac{1}{x+1}+\frac{5}{x-2}=\frac{3x}{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow\) \(\frac{x-2}{\left(x+1\right)\left(x-2\right)}+\frac{5\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\frac{3x}{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow\) x - 2 + 5x + 5 = 3x
\(\Leftrightarrow\) 6x + 3 - 3x = 0
\(\Leftrightarrow\) 3x + 3 = 0
\(\Leftrightarrow\) x = -1
Vậy S = {-1}