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\(\Rightarrow\left(x^2+2x+4\right)-x\left(x+1\right)⋮x+1\)
\(\Rightarrow\left(x^2+2x+4\right)-\left(x^2+x\right)⋮x+1\)
\(\Rightarrow x^2+2x+4-x^2-x⋮x+1\)
\(\Rightarrow x+4⋮x+1\)
\(\Rightarrow\left(x+4\right)-\left(x+1\right)⋮x+1\)
\(\Rightarrow x+4-x-1⋮x+1\)
\(\Rightarrow3⋮x+1\)
\(\Rightarrow x+1\inƯ\left(3\right)=\left(1;-1;3;-3\right)\)
Ta có bảng sau :
x + 1 1 -1 3 -3
x 0 -2 2 -4
Mà \(x\in Z\)
\(\Rightarrow x\in\left(0;-2;2;-4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Rightarrow\left(2-4x\right)+4\left(x-1\right)⋮x-1\)
\(\Rightarrow\left(2-4x\right)+\left(4x-4\right)⋮x-1\)
\(\Rightarrow2-4x+4x-4⋮x-1\)
\(\Rightarrow-2⋮x-1\)
\(\Rightarrow x-1\inƯ\left(-2\right)=\left(1;-1;2;-2\right)\)
Ta có bảng sau :
x - 1 1 -1 2 -2
x 2 0 3 -1
Mà \(x\in Z\)
\(\Rightarrow x\in\left(2;0;3;-1\right)\)
Vì (2-4x) chia hết cho x-1
suy ra 4(x-1)+2-4x
4x-4+2-4x = 6 chia hết cho x-1
suy ra x-1 thuộc B(6)={1;2;3;6}
x thuộc {2;3;4;7}
vậy x=2;3;4;7.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Rightarrow\left(3x+5\right)-3\left(x-2\right)⋮x-2\)
\(\Rightarrow\left(3x+5\right)-\left(3x-6\right)⋮x-2\)
\(\Rightarrow3x+5-3x+6⋮x-2\)
\(\Rightarrow11⋮x-2\)
\(\Rightarrow x-2\inƯ\left(11\right)=\left(1;-1;11;-11\right)\)
Ta có bảng sau :
x - 2 1 -1 11 -11
x 3 1 13 -9
Mà \(x\in Z\)
\(\Rightarrow x\in\left(3;1;13;-9\right)\)
Ta có : 3x + 5 = 3x-6+11
= 3(x-2)+11
Vì 3(x-2) chia hết cho x-2 nên 11 chia hết cho x-2
suy ra x-2 thuộc Ư(11) ={1:11}
suy ra x thuộc {3;13}
Vậy x = 3 hoặc 13
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1-\left(x-1\right):3=\dfrac{2}{3}\)
\(\Rightarrow1-\left(x-1\right)=\dfrac{2}{3}.3\)
\(\Rightarrow1-\left(x-1\right)=2\)
\(\Rightarrow x-1=1-2\)
\(\Rightarrow x-1=\left(-1\right)\)
\(\Rightarrow x=\left(-1\right)+1\)
\(\Rightarrow x=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{2x-1}{3}=\dfrac{2-x}{-2}\)
\(\Rightarrow-2\left(2x-1\right)=3\left(2-x\right)\)
\(\Rightarrow-4x+2=6-3x\Rightarrow x=-4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2/3.x + 1/4 = 7/12
2/3.x = 7/12 - 1/4
2/3.x = 1/3
x = 1/3 : 2/3
x = 1/2
Bài làm
\(\frac{2}{3}x+\frac{1}{4}=\frac{7}{12}\)
\(\frac{2}{3}x=\frac{7}{12}-\frac{1}{4}\)
\(\frac{2}{3}x=\frac{7}{12}-\frac{3}{12}\)
\(\frac{2}{3}x=\frac{4}{12}\)
\(\frac{2}{3}x=\frac{1}{3}\)
\(x=\frac{1}{3}:\frac{2}{3}\)
\(x=\frac{1}{3}.\frac{3}{2}\)
\(x=\frac{1}{2}\)
Vậy \(x=\frac{1}{2}\)
\(\Rightarrow\left(x^2-x+2\right)-x\left(x-1\right)⋮x-1\)
\(\Rightarrow\left(x^2-x+2\right)-\left(x^2-x\right)⋮x-1\)
\(\Rightarrow x^2-x+2-x^2+x⋮x-1\)
\(\Rightarrow2⋮x+1\)
\(\Rightarrow x+1\inƯ\left(2\right)=\left(1;-1;2;-2\right)\)
Ta có bảng sau :
x + 1 1 -1 2 -2
x 0 -2 1 -3
Mà \(x\in Z\)
\(\Rightarrow x\in\left(0;-2;1;-3\right)\)