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

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

a kham khảo nha , e nhờ a e lm chứ ko phải e lm nha ! 

\(\left(x-2\right)\left(\frac{3}{x}+2-\frac{5}{2x}-4+\frac{8}{x^2}-4\right)\)

\(\left(x-2\right)\left[\left(\frac{3}{x}-\frac{5}{2x}\right)-6+\frac{8}{x^2}\right]\)

\(\left(x-2\right)\left(\frac{1}{2x}-6+\frac{8}{x^2}\right)\)

\(\left(x-2\right)\left(\frac{3}{x+2}-\frac{5}{2x-4}+\frac{8}{x^2-4}\right)\)

\(=\left(x-2\right)\left[\frac{3}{x+2}-\frac{5}{2\left(x-2\right)}+\frac{8}{\left(x-2\right)\left(x+2\right)}\right]\)

\(=\left(x-2\right)\left[\frac{3.2\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{8.2}{2\left(x-2\right)\left(x+2\right)}\right]\)

\(=\left(x-2\right)\left[\frac{6\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{16}{2\left(x-2\right)\left(x+2\right)}\right]\)

\(=\left(x-2\right)\left[\frac{6\left(x-2\right)-5\left(x+2\right)+16}{2\left(x-2\right)\left(x+2\right)}\right]\)

\(=\frac{\left(x-2\right)\left(x-6\right)}{2\left(x-2\right)\left(x+2\right)}\)

\(=\frac{x-6}{2\left(x+2\right)}\)

a, ĐKXĐ:\(x^3+8\ne0\Rightarrow x^3\ne-8\Rightarrow x\ne-2\)

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

c, \(\dfrac{2}{x+2}=\dfrac{2}{2+2}=\dfrac{2}{4}=\dfrac{1}{2}\)

d, \(\dfrac{2}{x+2}>2\\ \Rightarrow2>2x+4\\ \Rightarrow2x+2< 0\\ \Rightarrow2x< -2\\ \Rightarrow x< -1\)

\(x^2-2x-8\)

=\(x^2-2x+1-9\)

=\((x-1)^2 -9\)

=(x-1-3)(x-1+3)

=(x-4)(x+2)

\(x^2-2x-8=\left(x-4\right)\left(x+2\right)\)

\(P=\frac{2x^2-8}{x-2}=\frac{2.\left(x^2-2^2\right)}{x-2}=\frac{2.\left(x-2\right).\left(x+2\right)}{x-2}=2x+4\left(x\ne2\right)\)

\(P=2x+4=2\Rightarrow2x=-2\Rightarrow x=-1\)

bài này dùng lược đồ Hooc-ne đoán nghiệm là ra 

\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)

\(=\dfrac{x^2-4x+2x-8}{2x^2+4x+5x+10}\)

\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)

\(=\dfrac{x-4}{2x+5}\)

Các bạn giúp mình với nhé thanks 

\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)

\(=\dfrac{\left(x-4\right)\left(x+2\right)}{2x^2+4x+5x+10}\)

\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)

\(=\dfrac{x-4}{2x+5}\)

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