Ta có : \(P=\frac{3n+2}{n-1}=\frac{3n-3+5}{n-1}=\frac{3\left(n-1\right)+5}{n-1}=3+\frac{5}{n-1}\)

Vì \(3\inℤ\Rightarrow\frac{5}{x-1}\inℤ\Rightarrow5⋮x-1\Rightarrow x-1\inƯ\left(5\right)\Rightarrow x-1\in\left\{1;5;-1;-5\right\}\)

=> \(x\in\left\{2;0;6;-4\right\}\)

Vậy  \(x\in\left\{2;0;6;-4\right\}\) là giá trị cần tìm

\(P=\frac{3n+2}{n-1}=\frac{3\left(n-1\right)+5}{n-1}=3+\frac{5}{n-1}\)

Để P đạt giá trị nguyên => \(\frac{5}{n-1}\)đạt giá trị nguyên

=> \(5⋮\left(n-1\right)\)

=> \(\left(n-1\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

+) n - 1 = 1 => n = 2

+) n - 1 = -1 => n = 0

+) n - 1 = 5 => n = 6

+) n - 1 = -5 => n = -4

Vậy \(n\in\left\{-4;0;2;6\right\}\)thì P có giá trị nguyên

2/3*|3/4-1.5|-1/1/6

=2/3*|3/4-3/2|-7/6

=2/3*|3/4-6/4|-7/6

=2/3*3/4-7/6

=1/2-7/6

=3/6-7/6

=-4/6=-2/3

a) \(\frac{1}{5}-\frac{1}{3}+\frac{2}{7}=\frac{21}{105}-\frac{35}{105}+\frac{30}{105}=\frac{16}{105}\)

b) \(\frac{1}{5}.\frac{3}{7}+\frac{4}{5}.\frac{3}{7}=\frac{3}{35}+\frac{12}{35}=\frac{15}{35}=\frac{3}{7}\)

c) \(\sqrt{16}:\sqrt{4}+\sqrt{9}=4:2+3=5\)

d)\(\left(\frac{-1}{4}\right)^4:\left(-\frac{1}{4}\right)=\left(\frac{-1}{4}\right)^3=\frac{-1}{64}\)

a. Ta có   D đối xứng với M qua N (gt)

           => MN = ND 

           => N là trung điểm của MD

Xét tứ giác ADCM , ta có:

           N là trung điểm của AC (gt)

           N là trung điểm của MD (cmt)

 => ADCM là hình bình hành (dhnb)

Mà AM là đường cao của tam giác ABC

 => AM vuông góc với BC => Góc M = 90^o 

Xét hình bình hành ADCM , ta có: Góc M = 90⁰

 => ADCM là hình chữ nhật (dhnb)

ĐK : \(x\ne0\)

Với \(3x-1-\frac{x-1}{4x}=\sqrt{3x+1}\), ta có :

\(3x-1-\frac{x-1}{4x}=\sqrt{3x^2-6x+1^2}=\sqrt{\left(3x-1\right)^2}\)

Thỏa mãn ĐK : \(3x-1=\sqrt{3x+1}\)

Với x là SC thì 3x - 1 và 3x + 1 là SL , với x là SL thì 3x - 1 và 3x + 1 là SC .

Miễn sao 3x - 1 và 3x + 1 cùng một x .

=> Xảy ra khi \(3x-1=\frac{\left(3x+1\right)}{2}\)

\(\Rightarrow x=1\)( min = max )

Complete the second sentence so that it has a same meaning to the first ơn. Use NO MORE THAN FOUR WORDS.

1. He has learnt English for three years.

-> English has been learnt for three years.

2. Minh really loves to hang out with friends.

-> Minh really enjoys hanging out with friends.

3. Jane cooks better than her sister.

-> Jane's sister cook isnot as good as Jane.

4. It takes four hours to go by car and five hours to go by train.

-> Going by train spends more time than going by car .

5. No one in my group is more intelligent than Mary.

-> Mary .is the most intelligent in my group.

6. Yesterday the temperature was nine degrees. Today it's only six degrees.

-> It's colder today than it was yesterday .

Complete each space with one of the words given below. Make changes if necessary.

   live        satisfaction         interviews         big          salary        optimis

A new survey has found that British people who live in the countryside are more (1)   optimis       than those who live in big cities. According to it, between January and September 2013, the (2)     salary ​        ratings of peole living in the countryside leapt from 20.5 to 30.8 per cent, an increase of five per cent compared to the previous year. These rural people all shared that the cost of (3)   living        , medical service and education had imroved significantly. As a result, they feel less pressure and enjoy life more. At the same time, people in big cities were worried and their confidence about job and the economy fell 3.9 per cent. The quatily of life, obtained from (4)       interviews      , was reported to be three times higher in the countryside than that in the city. Nevertheless, young people still prefer (5)      big        cities because of higher job demand, higher (6)       satisfaction             and more interesting life.