a, \(M=\sqrt{x^2-4x+4}-\sqrt{x^2+4x+4}\)      (ĐK : \(\forall x\in R\))

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

     * Nếu x\(\ge2\Rightarrow M=x-2-x-2=-4\)

     *Nếu x<2   => M=2-x-x-2=-2x

b,Để M=2\(\ne-4\)

     =>M=-2x

    =>-2x=-4

    =>x=2

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P=\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)

  \(=\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}\)

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

     * Nếu \(x\ge2\Rightarrow P=\sqrt{x-1}+1+\sqrt{x-1}-1=2\sqrt{x-1}\)

    * Nếu x<2  =>P=\(\sqrt{x-1}+1+1-\sqrt{x-1}=2\)

             VẬY.......

 Tk nha!

a) MTC = (x -2)(x + 2). Ta rút gọn được M = 1 x − 2  

b) Gợi ý:  x 2 + 5 x + 6 = ( x + 2 ) ( x + 3 ) ; x 2 + x − 12 = ( x − 3 ) ( x + 4 )

Ta có  N = ( x + 2 ) ( x + 3 ) ( x − 3 ) ( x + 4 ) : ( x + 2 ) 2 x ( x − 3 ) = x ( x + 3 ) ( x + 2 ) ( x + 4 )

`a)M=(x^4+2)/(x^6+1)+(x^2-1)/(x^4-x^2+1)-(x^2+3)/(x^4+4x^2+3)`

`=(x^4+2)/(x^6+1)+(x^2-1)/(x^4-x^2+1)-(x^2+3)/((x^2+1)(x^2+3))`

`=(x^4+2)/(x^6+1)+((x^2-1)(x^2+1))/(x^6+1)-1/(x^2+1)`

`=(x^4+2+x^4-1-x^4+x^2-1)/(x^2+1)`

`=(x^4+x^2)/(x^2+1)`

`=(x^2(x^2+1))/(x^2+1)`

`=x^2`

`b)` tìm gtnn chứ?

`M=x^2>=0`

Dấu '=" `<=>x=0`

a: |x-1|=3

=>x-1=3 hoặc x-1=-3

=>x=-2(nhận) hoặc x=4(loại)

Khi x=-2 thì \(A=\dfrac{4+4}{-2-4}=\dfrac{8}{-6}=\dfrac{-4}{3}\)

b: ĐKXĐ: x<>4; x<>-4

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

\(=\dfrac{-x^2-8x-16+x^2-8x+16-4x^2}{\left(x-4\right)\left(x+4\right)}=\dfrac{-4x^2-16x}{\left(x-4\right)\left(x+4\right)}\)

=-4x/x-4

c: A+B

=-4x/x-4+x^2+4/x-4

=(x-2)^2/(x-4)
A+B>0

=>x-4>0

=>x>4