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

Để biểu thức trên nhận giá trị âm khi \(\dfrac{\left(x-2\right)^2}{x^3-2x^2-4x+8}< 0\)

\(\Rightarrow x^3-2x^2-4x+8< 0\)do \(\left(x-2\right)^2\ge0\)

\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+4\right)-2x\left(x+2\right)< 0\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)^2< 0\Leftrightarrow x< -2\)

(-3).8/8.6 rút gọn

yggucbsgfuyvfbsudy

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Nguyên Đinh Huynh Ronaldo lúc nào cũng dễ

a: ĐKXĐ: x<>2; x<>0

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

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

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

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

c: M>=-3

=>(x+1+6x)/2x>=0

=>(7x+1)/x>=0

=>x>0 hoặc x<=-1/7

A = \(\left(3x-1\right)^2+2\left(3x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)

A = \(\left(3x-1+2x+1\right)^2\)

A)

<=>(3x)^2−2×3x+1+2(3x−1)(2x+1)+(2x+1)^2

<=>(3x)^2−2×3x+1+(6x−2)(2x+1)+(2x+1)^2

<=>(3x)^2−2×3x+1+12x^2+6x−4x−2+(2x+1)^2

<=>(3x)^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1

<=>32x^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1

<=>9x^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1

<=>9x^2−2×3x+1+12x^2+6x−4x−2+2^2x^2+2×2x+1

<=>9x^2−2×3x+1+12x^2+6x−4x−2+4x^2+2×2x+1

<=>9x^2−6x+1+12x^2+6x−4x−2+4x^2+2×2x+1

<=>9x^2−6x+1+12x^2+6x−4x−2+4x^2+4x+1

<=>(9x^2+12x^2+4x^2)+(−6x+6x−4x+4x)+(1−2+1)

<=> 25x^2

B)

<=>2x(4x^2−6x+9)+3(4x^2−6x+9)+8(1−x)(1+x+x^2)

<=>8x^3−12x^2+18x+3(4x^2−6x+9)+8(1−x)(1+x+x^2)

<=>8x^3−12x^2+18x+12x^2−18x+27+8(1−x)(1+x+x^2)

<=>8x^3−12x^2+18x+12x^2−18x+27+(8−8x)(1+x+x^2)

<=>8x^3−12x^2+18x+12x^2−18x+27+8(1+x+x^2)−8x(1+x+x^2)

<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−8x(1+x+x^2)

<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−(8x+8x2+8x^3)

<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−8x−8x^2−8x^3

<=>(8x^3−8x^3)+(−12x^2+12x^2+8x^2−8x^2)+(18x−18x+8x−8x)+(27+8)

<=> 35

đây là phân số hay sao bn