1: Sửa đề: 3x-5

\(=\dfrac{-x^2\left(3x-5\right)-3\left(3x-5\right)}{3x-5}=-x^2-3\)

2: \(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

=5x^2+14x^2+12x+8

3: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)

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

5: \(=\dfrac{x^2\left(5-3x\right)+3\left(5-3x\right)}{5-3x}=x^2+3\)

a: \(\dfrac{4x^4y-7x^2y+3y}{-3x^2+2y}\)

\(=\dfrac{4x^4y-4x^2y-3x^2y+3y}{-\left(3x^2-2y\right)}\)

\(=\dfrac{4x^2y\left(x^2-1\right)-3y\left(x^2-1\right)}{-\left(3x^2-2y\right)}\)

\(=\dfrac{y\left(x^2-1\right)\left(4x^2-3\right)}{-\left(3x^2-2y\right)}\)

a) `(4x^4y-7x^2y+3y).(2y-3x^2y)`

`=8x^4y^2-14x^2y^2+6y^2-12x^6y^2+21x^4y^2-9x^2y^2`

`=29x^4y^2-12x^6y^2-23x^2y^2+6y^2`

b) `(x^2+3x-3/2 x^3):2x - x/2 . (1-3/2 x)`

`=(x+3-3/2 x^2):2 - (x/2 - 3/4 x^2)`

`=x/2 + 3/2 - 3/4 x^2 -x/2 +3/4 x^2`

`=3/2`

c) `(-2x^3-x-3+5x^2):(3-2x)`

`=(3-2x)(x^2-x-1) : (3-2x)`

`=x^2-x-1`

c) Ta có: \(\dfrac{5x^4+9x^3-2x^2-4x-8}{x-1}\)

\(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

\(=\dfrac{5x^3\left(x-1\right)+14x^2\left(x-1\right)+12x\left(x-1\right)+8\left(x-1\right)}{x-1}\)

\(=5x^3+14x^2+12x+8\)

d) Ta có: \(\dfrac{5x^3+14x^2+12x+8}{x+2}\)

\(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}\)

\(=\dfrac{5x^2\left(x+2\right)+4x\left(x+2\right)+4\left(x+2\right)}{x+2}\)

\(=5x^2+4x+4\)

c) Ta có: \(\dfrac{5x^4+9x^3-2x^2-4x-8}{x-1}\)

\(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

\(=\dfrac{5x^3\left(x-1\right)+14x^2\left(x-1\right)+12x\left(x-1\right)+8\left(x-1\right)}{x-1}\)

\(=5x^3+14x^2+12x+8\)

a: \(\dfrac{2x^3-5x^2-x+1}{2x+1}\)

\(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}\)

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

b: \(\dfrac{x^3-2x+4}{x+2}\)

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

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

a,=x^2+2x

c,=x^2-1

f: \(=\dfrac{2x^3-10x^2-11x^2+55x+12x-60}{x-5}=2x^2-11x+12\)

a: \(=6x^3-10x^2+6x\)

b: \(=-2x^4-10x^3+6x^2\)

c: \(=-x^5+2x^3-\dfrac{3}{2}x^2\)

d: \(=2x^3+10x^2-8x-x^2-5x+4=2x^3+9x^2-13x+4\)