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

\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x};x\ne2;x\ne0\)

\(\Leftrightarrow\frac{x+2}{x-2}-\frac{1}{x}-\frac{2}{x^2-2x}=0\)

\(\Leftrightarrow\frac{x+2}{x-2}-\frac{1}{x}-\frac{2}{x\times\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x\times\left(x+2\right)-\left(x-2\right)-2}{x\times\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x\times\left(x+2\right)-x+2-2}{x\times\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x^2+2x-x}{x\left(x-2\right)}=0\)
\(\Leftrightarrow\frac{x^2+x}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x\left(x+1\right)}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x+1}{x-2}=0\Rightarrow x+1=0\)

\(\Rightarrow x=-1\)

1) y/(y + 2) - 3/(y - 2) = (y^2 + 8)/(y^2 - 4)

<=> y/(y + 2) - 3/(y - 2) = (y^2 + 8)/((y - 2)(y + 2))

<=> y(y - 2) - 3(y + 2) = y^2 + 8

<=> y^2 - 2y - 3y - 6 = y^2 + 8

<=> y^2 - 5y - 6 = y^2 + 8

<=> -5y - 6 = 8

<=> -5y = 8 + 6

<=> -5y = 14

<=> y = -14/5

2) 7/(2x - 3) + 1/(2x - 2) = 3/(x - 1)

<=> 14(x - 1) + 2x - 3 = 6(2x - 3)

<=> 14x - 14 + 2x - 3 = 12x - 18

<=> 16x - 17 = 12x - 18

<=> 16x - 17 - 12x = -18

<=> 4x - 17 = -18

<=> 4x = -18 + 17

<=> 4x = -1

<=> x = -1/4

a)\(6y\left(y-1\right)=y-1\)

\(6y=\frac{y-1}{y-1}\)

\(6y=1\)

\(y=\frac{1}{6}\)

b)  \(2\left(y+5\right)-y^2-5y=0\)

\(2y+10-y^2-5y=0\)

\(y\left(2-y-5\right)+10=0\)

\(y\left(-3-y\right)=-10\)

\(-3y-2y=-10\)

\(-5y=-10\)

\(y=2\)

c) \(y^3+y=0\)

\(y\left(y^2+1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}y=0\\y^2+1=0\end{cases}\Rightarrow\orbr{\begin{cases}y=0\\y^2=-1\left(vl\right)\end{cases}}}\)

hok tốt!!

Giải pt (1) :(x+3)(2x+1)=0

  =>{x+3=0   /     {2x+1=0

=> {x=-3   /      {x=-1/2 

Để hai pt tương đương thì pt (2) nhận giá trị x=-3 và x=-1/2 .

+)Thay x=-3 vào pt (2) :

     (m-4)(-3)^2 - 2(2m+9)(-3) -4 =0

=> (m-4)9 + 6(2m+9) - 4 = 0

=> 9m - 36+ 12m + 54 - 4= 0

=> 21m + 14 = 0

=> 21m = -14

=> m= -2/3

 Vậy ...

+) Thay x= -1/2 vào pt (2) :

     (m-4)(-1/2)^2 - 2(2m+9)(-1/2) -4 =0

=>1/4(m-4) + 2m +9 - 4 = 0

=>1/4m -1 +2m +9 - 4 =0

=>9/4m +4 =0

=>9/4m = -4 

=>m =-16/9

Vậy ...

\(A=\frac{2x^2+4x}{x^3-4x}+\frac{x^2-4}{x^2+2x}+\frac{2}{2-x}\left(x\ne0;x\ne\pm2\right)\)

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

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

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

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

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

Vậy \(A=\frac{-2x+8}{x\left(x-2\right)}\left(x\ne0;x\ne\pm2\right)\)

b) \(A=\frac{-2x+8}{x\left(x-2\right)}\left(x\ne0;x\ne\pm2\right)\)

Ta có: x=4 (tmđk) thay vào A ta có:

\(A=\frac{-2\cdot4+8}{4\left(4-2\right)}=\frac{-8+8}{4\cdot2}=\frac{0}{8}=0\)

Vậy A=0 với x=4