a) Ta có: \(B=\dfrac{x^2}{5x+25}+\dfrac{2\left(x+5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\)

\(=\dfrac{x^2}{5\left(x+5\right)}+\dfrac{2\left(x+5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\)

\(=\dfrac{x^3}{5x\left(x+5\right)}+\dfrac{10\left(x+5\right)^2}{5x\left(x+5\right)}+\dfrac{250+25x}{5x\left(x+5\right)}\)

\(=\dfrac{x^3+10x^2+100x+250+250+25x}{5x\left(x+5\right)}\)

\(=\dfrac{x^3+10x^2+125x+500}{5x\left(x+5\right)}\)

\(=\dfrac{x^3+5x^2+5x^2+25x+100x+500}{5x\left(x+5\right)}\)

\(=\dfrac{x^2\left(x+5\right)+5x\left(x+5\right)+100\left(x+5\right)}{5x\left(x+5\right)}\)

\(=\dfrac{\left(x+5\right)\left(x^2+5x+100\right)}{5x\left(x+5\right)}\)

\(=\dfrac{x^2+5x+100}{5x}\)

b) Thay x=-2 vào biểu thức \(B=\dfrac{x^2+5x+100}{5x}\), ta được:

\(B=\dfrac{\left(-2\right)^2+5\cdot\left(-2\right)+100}{-5\cdot2}=\dfrac{4+100-10}{-10}=\dfrac{94}{-10}=-\dfrac{94}{10}=\dfrac{-47}{5}\)

Vậy: Khi x=-2 thì \(B=-\dfrac{47}{5}\)

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 )

b: \(x-2\sqrt{xy}+y=\left(\sqrt{x}-\sqrt{y}\right)^2\)

Giúp tớ với

Với x > 0;x ≠ 1 ta có:

A = x + 3 x x + 1 - x - 3 x x - 1

= x + 3 x - 1 - x - 3 x + 1 x x - 1 x + 1 = x + 2 x - 3 - x - 2 x - 3 x x - 1 = 4 x x x - 1 = 4 x - 1