`!`

`(x^3-3x^2):(x-3)`         

`= x^2(x-3)  :(x-3)` 

`=x^2`

`----`

`(2x^2+2x-4):(x+2)`

`=2(x^2+x-2) :(x+2)`

`= 2 (x^2+2x-x-2) :(x+2)`

\(=2\left[x\left(x+2\right)-\left(x+2\right)\right]:\left(x+2\right)\)

`= 2(x+2)(x-1) :(x+2)`

`=2(x-1)`

`-------`

`(x^4-x-14):(x-2)`

https://hoc24.vn/cau-hoi/x4-x-14-x-2-giup-minh.204306769717

bn tham khảo ở đây nha

`----`

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

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

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

`=x^2+1`

a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)

\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)

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

b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)

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

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

d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)

\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)

\(=x^2-2x-5\)

a, \(\left(2x^3-x^2+5x\right):x=2x^2-x+5\)

b, \(\left(3x^4-2x^3+x^2\right):\left(-2x\right)=-\frac{3}{2}x^3+x^2-\frac{1}{2}x\)

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

\(\left(3x^4-2x^3+x^2\right):\left(-2x\right)=[3x^4:\left(-2x\right)]+[-2x^3:\left(-2x\right)]+[x^2:\left(-2x\right)]=-\frac{3}{2}x^3+x^2-\frac{x}{2}\)

a: \(=2x^2-4x-6x+12-2x^2+10x=12\)

a: \(=\dfrac{5}{2x^2y}+\dfrac{2}{3xy}-\dfrac{y}{x^3}\)

\(=\dfrac{5\cdot3\cdot x}{6x^3y}+\dfrac{2\cdot2\cdot x^2}{6x^3y}-\dfrac{6y^2}{6x^3y}\)

\(=\dfrac{15x+4x^2-6y^2}{6x^3y}\)

b: \(=\dfrac{2x-7+3x+5}{10x-4}=\dfrac{5x-2}{10x-4}=\dfrac{1}{2}\)

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

`a)3x(2x^2-3x+4)`

`=6x^3-9x^2+12x`

______________________________________________

`b)(x+3)^2+(3x-2)(x+4)`

`=x^2+6x+9+3x^2+12x-2x-8`

`=4x^2+16x+1`

______________________________________________

`c)[2x-4]/[x-1]+[2x+2]/[x^2-1]`       `ĐK: x \ne +-1`

`=[(2x-4)(x+1)+2x+2]/[(x-1)(x+1)]`

`=[2x^2+2x-4x-4+2x+2]/[(x-1)(x+1)]`

`=[2x^2-2]/[x^2-1]`

`=2`

hếp

Bài 1: 

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

Bài 2: 

a: \(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)

\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)

d: \(=\dfrac{3}{2x^2y}+\dfrac{5}{xy^2}+\dfrac{x}{y^3}\)

\(=\dfrac{3y^2+10xy+2x^3}{2x^2y^3}\)

e: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2x^2-4xy}{\left(x+2y\right)\cdot\left(x-2y\right)}=\dfrac{2x}{x+2y}\)

a: \(=2x^3:\dfrac{-3}{2}x+4x:\dfrac{3}{2}x-5:\dfrac{3}{2}\)

=-4/3x^2+8/3-10/3

=-4/3x^2-2/3

d: \(\dfrac{3x^3-5x+2}{x-3}=\dfrac{3x^3-9x^2+9x^2-27x+22x-66+68}{x-3}\)

\(=3x^2+9x+22+\dfrac{68}{x-3}\)