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