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

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

Khi \(x=-\dfrac{3}{2}\Rightarrow M=\dfrac{-\dfrac{3}{2}+2}{-\dfrac{3}{2}}=-\dfrac{1}{3}\)

Bài 3:

Ta có: \(2n^2+n-7⋮n-2\)

\(\Leftrightarrow2n^2-4n+5n-10+3⋮n-2\)

\(\Leftrightarrow n-2\in\left\{1;-1;3;-3\right\}\)

hay \(n\in\left\{3;1;5;-1\right\}\)

\(Bài.44:\\ a,3x-7=0\\ \Leftrightarrow3x=7\\ \Leftrightarrow x=\dfrac{7}{3}\\ b.2x^2+9=0\\ \Leftrightarrow x^2=-\dfrac{9}{2}\left(vô.lí\right)\\ \Rightarrow Không.có.x.thoả.mãn\)

43:

a: \(A=2x\left(x^2-2x-3\right)-6x^2+5x-1+9x^2+3x+3\)

\(=2x^3-4x^2-6x+3x^2+8x+2\)

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

b: \(\dfrac{A}{2x-1}=\dfrac{x^2\left(2x-1\right)+2x-1+3}{2x-1}=x^2+1+\dfrac{3}{2x-1}\)

Thương là x^2+1

Dư là 3

c: A chia hết cho 2x-1

=>3 chia hết cho 2x-1

=>2x-1 thuộc {1;-1;3;-3}

=>x thuộc {1;0;2;-1}

`a,`

`P(x)=5x^3+3-3x^2+x^4-2x-2+2x^2+x`

`P(x)=x^4+5x^3+(-3x^2+2x^2)+(-2x+x)+(3-2)`

`P(x)=x^4+5x^3-x^2-x+1`

`Q(x)=2x^4+x^2+2x+2-3x^2-5x+2x^3-x^4`

`Q(x)=(2x^4-x^4)+2x^3+(x^2-3x^2)+(2x-5x)+2`

`Q(x)=x^4+2x^3-2x^2-3x+2`

`b,`

`P(x)-Q(x)=(x^4+5x^3-x^2-x+1)-(x^4+2x^3-2x^2-3x+2)`

`P(x)-Q(x)= x^4+5x^3-x^2-x+1-x^4-2x^3+2x^2+3x-2`

`P(x)-Q(x)=(x^4-x^4)+(5x^3-2x^3)+(-x^2+2x^2)+(-x+3x)+(1-2)`

`P(x)-Q(x)=3x^3+x^2+2x-1`

b: \(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)

\(=2x^2-3x+1\)

a: \(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)

\(=2x^2-3x+1\)

B   =   x 6   –   2 x 4   +   x 3   +   x 2   –   x     ⇔   B   =   x 6   –   x 4   –   x 4   +   x 3   +   x 2   –   x     ⇔   B   =   ( x 6   –   x 4 )   –   ( x 4   –   x 2 )   +   ( x 3   –   x )     ⇔   B   =   x 3 ( x 3   –   x )   –   x ( x 3   –   x )   +   ( x 3   –   x )     ⇔   B   =   ( x 3   –   x   +   1 ) ( x 3   –   x )

Tại x 3 – x = 6, ta có B = (6 + 1).6 = 7.6 = 42

Đáp án cần chọn là: B

B   =   x 6   –   2 x 4   +   x 3   +   x 2   –   x     ⇔   B   =   x 6   –   x 4   –   x 4   +   x 3   +   x 2   –   x     ⇔   B   =   ( x 6   –   x 4 )   –   ( x 4   –   x 2 )   +   ( x 3   –   x )     ⇔   B   =   x 3 ( x 3   –   x )   –   x ( x 3   –   x )   +   ( x 3   –   x )     ⇔   B   =   ( x 3   –   x   +   1 ) ( x 3   –   x )

Tại x 3 – x = 6, ta có B = (6 + 1).6 = 7.6 = 42

Đáp án cần chọn là: B

\(1,\\ a,A=4x^2\left(-3x^2+1\right)+6x^2\left(2x^2-1\right)+x^2\\ A=-12x^4+4x^2+12x^2-6x^2+x^2=-x^2=-\left(-1\right)^2=-1\\ b,B=x^2\left(-2y^3-2y^2+1\right)-2y^2\left(x^2y+x^2\right)\\ B=-2x^2y^3-2x^2y^2+x^2-2x^2y^3-2x^2y^2\\ B=-4x^2y^3-4x^2y^2+x^2\\ B=-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^3-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^2+\left(0,5\right)^2\\ B=\dfrac{1}{8}-\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{8}\)

\(2,\\ a,\Leftrightarrow10x-16-12x+15=12x-16+11\\ \Leftrightarrow-14x=-4\\ \Leftrightarrow x=\dfrac{2}{7}\\ b,\Leftrightarrow12x^2-4x^3+3x^3-12x^2=8\\ \Leftrightarrow-x^3=8=-2^3\\ \Leftrightarrow x=2\\ c,\Leftrightarrow4x^2\left(4x-2\right)-x^3+8x^2=15\\ \Leftrightarrow16x^3-8x^2-x^3+8x^2=15\\ \Leftrightarrow15x^3=15\\ \Leftrightarrow x^3=1\Leftrightarrow x=1\)

\(P=x\left(2x+1\right)-x^2\left(x+2\right)+x^3-x+3\\ P=2x^2+x-x^3-2x^2+x^3-x+3\\ P=3\left(đfcm\right)\)