a) \(E=\left(\frac{1}{x+2}+\frac{1}{x-2}\right).\frac{x-2}{x}\left(ĐKXĐ:x\ne0;x\ne\pm2\right)\)

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

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

b) Khi x = 6 \(\Rightarrow E=\frac{2}{x+2}=\frac{2}{6+2}=\frac{2}{8}=\frac{1}{4}\)

c) \(E=4\Leftrightarrow\frac{2}{x+2}=4\Leftrightarrow4\left(x+2\right)=2\Leftrightarrow4x+8=2\Leftrightarrow x=\frac{-3}{2}\)

Vậy để E = 4 thì x = -3/2

d) \(E>0\Leftrightarrow\frac{2}{x+2}>0\Leftrightarrow2>0\)

Vậy phương trình vô nghiệm

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

Nếu x + 2 = 1 thì x = -1

Nếu x + 2 = -1 thì  x = -3

Nếu x + 2 = 2 thì x = 0

Nếu x + 2 = -2 thì x = -4

Vậy ...

Nek bạn giải thích hộ mik tí nữa nhé :Tại sao  2 > 0 thì phương trình lại vô nghiệm ?

a)  \(\left(x+2y\right)^2=x^2+4xy+4y^2\)

b)  \(\left(x-3y\right)\left(x+3y\right)=x^2-9y^2\)

c)  \(\left(5-x\right)=25-10x+x^2\)

a) \(\left(x+2y\right)^2=x^2+2.x.2y+\left(2y\right)^2=x^2+4xy+4y^2\)

b) \(\left(x-3y\right)\left(x+3y\right)=x^2-\left(3y\right)^2=x^2-9y^2\)

c) \(\left(5-x\right)^2=5^2-2.x.5+x^2=25-10x+x^2\)

a)  mk chỉnh đề

 \(978^2+22^2+978.44=\left(978+22\right)^2=100^2=10000\)

b)   \(52.48=\left(50+2\right)\left(50-2\right)=50^2-2^2=2496\)

c) mk chỉnh đề

  \(821^2+321^2-821.642=\left(821-321\right)^2=500^2=250000\)

a) \(978^2+22^2+978.44=978^2+2.22.978+22^2=\left(978+22\right)^2=1000^2=1000000\)

b) \(52.48=\left(50+2\right).\left(50-2\right)=50^2-2^2=2500-4=2496\)

c) Có nhầm dấu không bạn ơi. Mình sửa luôn nha

821² + 321² - 821.642 = 821² - 2.821.321 + 321² = (821-321)² = 500² = 250 000

b) \(\left(x+3\right)\left(x^2-3x+9\right)-x^3=2x\)

\(\Leftrightarrow x^3+3^3-x^3-2x=0\)

\(\Leftrightarrow27-2x=0\)

\(\Leftrightarrow2x=27\)

\(\Leftrightarrow x=\frac{27}{2}=13,5\)

c) \(\left(x-2\right)^3-x^3+6x^2=7\)

\\(\Leftrightarrow x^3-3.x^2.2+3.x.2^2-2^3-x^3+6x^2=7\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+6x^2-7=0\)

\(\Leftrightarrow12x=15\Leftrightarrow x=\frac{15}{12}=\frac{5}{4}=1,25\)