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29 tháng 12 2020

\(A=\frac{x+1}{x-2}+\frac{x-1}{x+2}+\frac{x^2+4x}{4-x^2}\)

a) \(=\frac{x+1}{x-2}+\frac{x-1}{x+2}-\frac{x^2+4x}{x^2-4}\)

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

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

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

\(=\frac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\frac{x-2}{x+2}\)

b) Tại x = 4 thỏa mãn x ≠ ±2 => A = 1/3

c) Ta có \(A=\frac{x-2}{x+2}=\frac{x+2-4}{x+2}=1-\frac{4}{x+2}\)

Để A nhận giá trị nguyên dương thì \(\frac{4}{x+2}\)nguyên

=> 4 chia hết cho x+2

=> x + 2 thuộc Ư(4) = { ±1 ; ±2 ; ±4 }

x+21-12-24-4
x-1-30-42-6

Rồi bạn thử từng cái vô xem cái nào làm cho A dương thì lấy

24 tháng 2 2017

AH
Akai Haruma
Giáo viên
29 tháng 12 2022

Bạn nên viết đề bằng công thức toán để được hỗ trợ tốt hơn (biểu tượng $\sum$ góc trái khung soạn thảo). 

29 tháng 12 2022

\(A=\left(\dfrac{x}{x-2}+\dfrac{12}{x^2-4}-\dfrac{x}{x+2}\right):\dfrac{4}{x-2}\left(x\ne2;x\ne-2\right)\)

\(a,A=\left(\dfrac{x}{x-2}+\dfrac{12}{x^2-4}-\dfrac{x}{x+2}\right):\dfrac{4}{x-2}\)

\(=\left[\dfrac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{12}{\left(x-2\right)\left(x+2\right)}-\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\right]:\dfrac{4}{x-2}\)

\(=\left[\dfrac{x^2+2x+12-x^2+2x}{\left(x-2\right)\left(x+2\right)}\right]:\dfrac{4}{x-2}\)

\(=\dfrac{4x+12}{\left(x-2\right)\left(x+2\right)}:\dfrac{4}{x-2}\)

\(=\dfrac{4\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}.\dfrac{x-2}{4}\)

\(=\dfrac{x+3}{x+2}\)

\(b,x=-1\Rightarrow A=\dfrac{\left(-1\right)+3}{\left(-1\right)+2}=2\)

\(c,A=\dfrac{x+3}{x+2}=\dfrac{x+2+1}{x+2}=1+\dfrac{1}{x+2}\)

\(A\in Z\Leftrightarrow x+2\inƯ\left(1\right)=\left\{1;-1\right\}\)

\(\Rightarrow x\in\left\{-1;-3\right\}\) (thỏa mãn điều kiện)

20 tháng 12 2019

a) Ta có: A = \(\frac{x+1}{x-2}+\frac{x-1}{x+2}+\frac{x^2+4x}{4-x^2}\)

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

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

A = \(\frac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}\)

A = \(\frac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\frac{x-2}{x+2}\)

b) Với x = 4 => A = \(\frac{4-2}{4+2}=\frac{2}{8}=\frac{1}{4}\)

c) ĐKXĐ: \(\hept{\begin{cases}x-2\ne0\\x+2\ne0\\4-x^2\ne0\end{cases}}\) <=> \(\hept{\begin{cases}x\ne2\\x\ne-2\\x\ne\pm2\end{cases}}\) <=> \(x\ne\pm2\)

Ta có: A = \(\frac{x-2}{x+2}=\frac{\left(x+2\right)-4}{x+2}=1-\frac{4}{x+2}\)

Để A  nhận giá trị nguyên dương <=> \(1-\frac{4}{x+2}\) nguyên dương

<=> \(-\frac{4}{x+2}\) nguyên dương <=> -4 \(⋮\)x + 2

 <=> x + 2 \(\in\)Ư(-4) = {1; -1; 2; -2; 4; -4}

Lập bảng: 

x + 2 1 -1 2 -2 4 -4
  x-1(tm)-3(tm)0(tm)-4(tm) 2(ktm)-6(tm)

Vậy ....

a: \(A=\left(\dfrac{x}{x^2-4}+\dfrac{4}{x-2}+\dfrac{1}{x+2}\right):\dfrac{3x+3}{x^2+2x}\)

\(=\dfrac{x+4x+8+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x+2\right)}{3\left(x+1\right)}\)

\(=\dfrac{6\left(x+1\right)\cdot x\left(x+2\right)}{3\left(x+1\right)\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{2x}{x-2}\)

22 tháng 12 2022

loading...

a: Khi x=5 thì A=5/(5+3)=5/8

b: \(C=A+B=\dfrac{x}{x+3}+\dfrac{2}{x-3}+\dfrac{3-5x}{x^2-9}\)

\(=\dfrac{x^2-3x+2x+6+3-5x}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}=\dfrac{x-3}{x+3}\)

c: Để C nguyên thì x+3-6 chia hết cho x+3

=>\(x+3\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

=>\(x\in\left\{-2;-4;-1;-5;0;-6;-9\right\}\)

a: \(P=\dfrac{x^2-x-18+2x+6-4x+12}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{x^2-3x}{\left(x-3\right)\left(x+3\right)}=\dfrac{x}{x+3}\)

b: P=2/3

=>x/(x+3)=2/3

=>3x=2x+6

=>x=6(nhận)

c: P nguyên

=>x chia hết cho x+3

=>x+3-3 chia hết cho x+3

=>x+3 thuộc {1;-1;2;-2}

=>x thuộc {-2;-4;-1;-5}

29 tháng 12 2021

a: \(A=\dfrac{x^2-2x+2x^2+4x-3x^2-4}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x-4}{\left(x-2\right)\left(x+2\right)}=\dfrac{2}{x+2}\)

5 tháng 1 2023

a, \(\dfrac{x}{x+2}\) + \(\dfrac{2x}{x-2}\) -\(\dfrac{3x^2-4}{x^2-4}\)

\(\dfrac{x}{x+2}+\dfrac{2x}{x-2}-\dfrac{3x^2+4}{x^2-4}\)

\(\dfrac{x}{x+2}+\dfrac{2x}{x-2}-\dfrac{3x^2+4}{\left(x+2\right)\left(x-2\right)}\)

\(\dfrac{x\left(x-2\right)+2x\left(x+2\right)-3x^2-4}{\left(x+2\right)\left(x-2\right)}\)

\(\dfrac{2x-4}{\left(x+2\right)\left(x-2\right)}=\dfrac{2\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{2}{x+2}\)

Có vài bước mình làm tắc á nha :>

27 tháng 7 2021

nhanh giùm mình được không

 

Bài 1: 

a) Ta có: \(P=1+\dfrac{3}{x^2+5x+6}:\left(\dfrac{8x^2}{4x^3-8x^2}-\dfrac{3x}{3x^2-12}-\dfrac{1}{x+2}\right)\)

\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\left(\dfrac{8x^2}{4x^2\left(x-2\right)}-\dfrac{3x}{3\left(x-2\right)\left(x+2\right)}-\dfrac{1}{x+2}\right)\)

\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\left(\dfrac{4}{x-2}-\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{1}{x+2}\right)\)

\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\dfrac{4\left(x+2\right)-x-\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{4x+8-x-x+2}\)

\(=1+3\cdot\dfrac{\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)

\(=1+\dfrac{3\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)

\(=\dfrac{\left(x+3\right)\left(2x+10\right)+3\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)

\(=\dfrac{2x^2+10x+6x+30+3x-6}{\left(x+3\right)\left(2x+10\right)}\)

\(=\dfrac{2x^2+19x-6}{\left(x+3\right)\left(2x+10\right)}\)