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b,
Ta có:
TH2: n-2= -1 \(\Rightarrow n=1\)
TH3: n-2 = 1\(\Rightarrow n=3\)
TH4: n- 2 = 3\(\Rightarrow n=5\)
Vậy n\(\in\left\{-1;1;3;5\right\}\)thì \(\dfrac{n-1}{n-2}\)
Bài 1:
a: Để A là phân số thì n+1<>0
hay n<>-1
b: Để A là số nguyên thì \(n+1\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{0;-2;4;-6\right\}\)
Bài 1:
a: Để A là số nguyên thì \(x+1⋮3\)
=>x=3k-1, với k là số nguyên
b; Để B là số nguyên thì \(x-1\in\left\{1;-1;17;-17\right\}\)
hay \(x\in\left\{2;0;18;-16\right\}\)
a) Để A có giá trị nguyên
\(\Rightarrow\frac{3}{x-1}\in z\Rightarrow3⋮x-1\)
\(\Rightarrow x-1\inƯ_{\left(3\right)}=\left(3;-3;1;-1\right)\)
nếu x-1 = 3 => x = 4 (TM)
x-1 = - 3 => x = -2 (TM)
x -1 = 1 => x = 2 (TM)
x -1 = -1 => x = 0 (TM)
KL: x = ....
b) ta có: \(\frac{x-2}{x+3}=\frac{x+3-5}{x+3}=\frac{x+3}{x+3}-\frac{5}{x+3}=1-\frac{5}{x+3}\)
Để B có giá trị nguyên
\(\Rightarrow\frac{5}{x+3}\in z\)
\(\Rightarrow5⋮x+3\Rightarrow x+3\inƯ_{\left(5\right)}=\left(5;-5;1;-1\right)\)
nếu x+3 = 5 => x = 2(TM)
x +3 = -5 => x = -8 (TM)
x +3 = 1 => x = -2 (TM)
x+3 = -1 => x = -4 (TM)
KL: x =.....
c) ta có: \(\frac{2x+1}{x-3}=\frac{2x-6+7}{x-3}=\frac{2.\left(x-3\right)+7}{x-3}=\frac{2.\left(x-3\right)}{x-3}+\frac{7}{x-3}=2+\frac{7}{x-3}\)
Để C có giá trị nguyên
\(\Rightarrow\frac{7}{x-3}\in z\)
\(\Rightarrow7⋮x-3\Rightarrow x-3\inƯ_{\left(7\right)}=\left(7;-7;1;-1\right)\)
nếu x -3 = 7 => x = 10 (TM)
x -3 = - 7 => x = -4 (TM)
x -3 = 1 => x =4 (TM)
x -3 = -1 => x = 2 (TM)
KL: x =...
d) ta có: \(\frac{x^2-1}{x+1}=\frac{x^2+x-x+1}{x+1}=\frac{x.\left(x+1\right)-(x+1)+1}{x+1}\)
\(=\frac{x.\left(x+1\right)}{x+1}-\frac{x+1}{x+1}+\frac{1}{x+1}=x-1+\frac{1}{x+1}\) ( x thuộc Z)
Để D có giá trị nguyên
\(\Rightarrow\frac{1}{x+1}\in z\)
\(\Rightarrow1⋮x+1\Rightarrow x+1\inƯ_{\left(1\right)}=\left(1;-1\right)\)
nếu x +1 = 1 => x =1 (TM)
x +1 = -1 => x = -2 (TM)
KL: x = ....
Chúc bn học tốt !!!!!!
Hoàn tất đoạn văn sau, sau đó trả lời câu hỏi bên dưới
Quang s camping(1)_______at_____the weekend, he often go camping(2)_____on_____the mountains. He usually goes(3)____with______ his friend. Quang and his fried always wear strong boots(4)_____and______warm clothes. (5)______They_____always take food, water and a camping stove. Sometimes, they (6)______camp_______overnight.
* Questions:
1. What does Quang s?
He s camping.
2. Where does he often go camping?
He often goes camping on the mountains.
3. When does he go?
On weekend.
4. Who does he usually go with?
He usually goes with his friend.
5. What do they always wear?
Quang and his fried always wear strong boots and warm clothes.
6. What do they always take?
They always take food, water and a camping stove.
7. Do they camp overnight?
Yes, they do.
Ta có:
\(A=\dfrac{3n+2}{n-1}=\dfrac{3\left(n-1\right)+5}{n-1}=\dfrac{3\left(n-1\right)}{n-1}+\dfrac{5}{n-1}\)
Để \(A\in Z\) thì \(5⋮n-1\) hay \(n-1\in U\left(5\right)=\left\{\pm1;\pm5\right\}\)
Lập bảng giá trị:
| \(n-1\) | \(1\) | \(-1\) | \(5\) | \(-5\) |
| \(n\) | \(2\) | \(0\) | \(6\) | \(-4\) |
d) Câu hỏi của Kudo Son - Toán lớp 6 | Học trực tuyến
e) Để \(E\in Z\)
thì \(n+2⋮n-5\)
\(\Rightarrow\left(n-5\right)+7⋮n-5\)
mà \(n-5⋮n-5\Rightarrow7⋮n-5\)
\(\Rightarrow n-5\inƯ\left(7\right)\)
\(\Rightarrow n-5\in\left\{\pm1;\pm7\right\}\)
+) \(n-5=1\Rightarrow n=6\left(tm\right)\)
+) \(n-5=-1\Rightarrow n=4\left(tm\right)\)
+) \(n-5=7\Rightarrow n=12\left(tm\right)\)
+) \(n-5=-7\Rightarrow n=-2\left(tm\right)\)
Vậy \(n\in\left\{6;4;12;-2\right\}\).