Phân tích đa thức thành nhân tử

a) 2( x + 1 ) - 3y( x + 1 ) = ( x + 1 )( 2 - 3y )

b) x² - 5x + 4 = x² - x - 4x + 4 = x( x - 1 ) - 4( x - 1 ) = ( x - 1 )( x - 4 )

Tìm x

a) x( x - 3 ) + 7x - 21 = 0

<=> x( x - 3 ) + 7( x - 3 ) = 0

<=> ( x - 3 )( x + 7 ) = 0

<=> x - 3 = 0 hoặc x + 7 = 0

<=> x = 3 hoặc x = -7

b) ( x - 2 )² + x( 3 - x ) = 6

<=> x² - 4x + 4 + 3x - x² = 6

<=> -x + 4 = 6

<=> -x = 2

<=> x = -2

\(A=\frac{x-2}{x}\)và \(B=\frac{x}{x-2}-\frac{2x}{x^2-4}\)( x ≠ 0 ; x ≠ ±3 )

a) Tại x = 23 ( tmđk ) => \(A=\frac{23-2}{23}=\frac{21}{23}\)

b) P = A.B

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

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

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

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

Để P = 4 => \(\frac{x}{x+2}=4\)

=> 4( x + 2 ) = x

=> 4x + 8 - x = 0

=> 3x + 8 = 0

=> x = -8/3 ( tmđk )

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

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

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

\(\frac{2x-1}{2x}+\frac{2x}{1-2x}+\frac{1}{4x^2-2x}\)

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

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

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

\(=\frac{-4x+2}{2x\left(2x-1\right)}=\frac{-2\left(2x-1\right)}{2x\left(2x-1\right)}=-\frac{1}{x}\)

em mới học đến lớp 5 nên ko giải được ạ!