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Đề đâu??????

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

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

\(=\dfrac{5x^2+4x+4-4+4x-x^2}{\left(2+x\right)}\cdot\dfrac{1}{2\left(x-3\right)}\)

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

b: |x-2|=2

=>x-2=2 hoặc x-2=-2

=>x=0(nhận) hoặc x=4(nhận)

Khi x=0 thì \(A=\dfrac{2\cdot0}{0-3}=\dfrac{-2}{3}\)

Khi x=4 thì \(A=\dfrac{2\cdot4}{4-3}=8\)

c: A>0

=>x/x-3>0

=>x>3 hoặc x<0

=>x>3

Đề sai rồi bạn

Sửa đề: f(x) = x² - 4x + 3

a) f(0) = 0 - 4.0 + 3 = 3

f(1) = 1 - 4.1 + 3 = 0

f(3) = 9 - 4.3 + 3 = 0

b) x = 1 và x = 3 là nghiệm của đa thức f(x) vì f(1) = 0 và f(3) = 0

a: Ta có: \(N=\dfrac{x^3-1}{x^2-2x+1}\)

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

\(=\dfrac{x^2+x+1}{x-1}\)

\(=\dfrac{\left(-1\right)^2+\left(-1\right)+1}{-1-1}=\dfrac{1}{-2}=-\dfrac{1}{2}\)

b: Ta có: \(M=\dfrac{x^3+8}{x^2-2x+4}\)

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

\(=x+2=0\)

a) \(N=\dfrac{x^3-1}{x^2-2x+1}=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{\left(x-1\right)^2}=\dfrac{x^2+x+1}{x-1}=\dfrac{\left(-1\right)^2-1+1}{-1-1}=-\dfrac{1}{2}\)b) \(M=\dfrac{x^3+8}{x^2-2x+4}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x^2-2x+4}=x+2=-2+2=0\)

a, ĐKXĐ: x≠±2

A=\(\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right)\left(x-2+\dfrac{10-x^2}{x+2}\right)\)

A=\(\left(\dfrac{x}{x^2-4}-\dfrac{2x+4}{x^2-4}+\dfrac{x-2}{x^2-4}\right)\left(\dfrac{x^2+2x}{x+2}-\dfrac{2x+4}{x+2}+\dfrac{10-x^2}{x+2}\right)\)

A=\(\left(\dfrac{-6}{x^2-4}\right)\left(\dfrac{6}{x+2}\right)\)

A=\(\dfrac{-36}{\left(x-2\right)\left(x+2\right)^2}\)

b, |x|=\(\dfrac{1}{2}\)

TH1z: x≥0 ⇔ x=\(\dfrac{1}{2}\) (TMĐKXĐ)

TH2: x<0 ⇔ x=\(\dfrac{-1}{2}\) (TMĐXĐ)

Thay \(\dfrac{1}{2}\), \(\dfrac{-1}{2}\) vào A ta có:

\(\dfrac{-36}{\left(\dfrac{1}{2}-2\right)\left(\dfrac{1}{2}+2\right)^2}\)=\(\dfrac{96}{25}\)

\(\dfrac{-36}{\left(\dfrac{-1}{2}-2\right)\left(\dfrac{-1}{2}+2\right)^2}\)=\(\dfrac{32}{5}\)

c, A<0 ⇔ \(\dfrac{-36}{\left(x-2\right)\left(x+2\right)^2}\) ⇔ (x-2)(x+2)² < 0

⇔   {x-2>0        ⇔      {x>2

     [                           [

       {x+2<0                 {x<2

⇔   {x-2<0        ⇔      {x<2

     [                           [

       {x+2>0                 {x>2

⇔ x<2 

Vậy x<2 (trừ -2)

a, ĐKXĐ: x≠±3

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

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

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

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

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

A=\(\dfrac{-1}{x^2}\)

b, Thay x=\(-\dfrac{1}{2}\) (TMĐKXĐ) vào A ta có:

\(\dfrac{-1}{\left(-\dfrac{1}{2}\right)^2}\)=-4

c, A<0 ⇔ \(\dfrac{-1}{x^2}< 0\) ⇔ x²>0 (Đúng với mọi x)

Vậy để A<0 thì x đúng với mọi giá trị (trừ ±3)