\(\left(4x^2y^3+7xy^5-9x^6y^2\right):2xy^2\)

\(=\frac{4x^2y^3}{2xy^2}+\frac{7xy^5}{2xy^2}-\frac{9x^6y^2}{2xy^2}=2xy+\frac{7}{2}y^3-\frac{9}{2}x^5\)

Bài 3:

3: \(6x\left(x-y\right)-9y^2+9xy\)

\(=6x\left(x-y\right)+9xy-9y^2\)

\(=6x\left(x-y\right)+9y\left(x-y\right)\)

\(=\left(x-y\right)\left(6x+9y\right)\)

\(=3\left(2x+3y\right)\left(x-y\right)\)

Bài 4:

a/ 5x²y (x²y– 4xy² + 7xy)

`=5x^4y^2-20x^3y^3+35x^3y^2`

b/ 3xy² (x²y³ + x 2y – xy² )

`=3x^3y^5+3x^3y^3-3x^2y^4`

c/ 3x(12x² + 4x – 5) + 2x(9x² – 6x + 7)

`=36x^3+12x^2-15x+18x^3-18x^2+14x`

`=54x^3-6x^2-x`

d/ 5x(2x² – 9x – 5) – 9x (x² - 7x – 4)

`=10x^3-45x^2-25x-9x^3+63x^2+36x`

`=x^3+18x^2+11x`

a, \(=12x^5+9x^3y^2-6x^2y^3-20x^4y-15x^2y^3-10xy^4-24x^3y^2-18xy^4+12y^5\)

(tự rút gọn cái :P)

b, \(8x^3+4x^2y-2xy^2-y^3\)

\(=4x^2\left(2x+y\right)-y^2\left(2x+y\right)=\left(2x+y\right)^2\left(2x-y\right)\)

\(4x^2y^2-4x^2-4xy-y^2=4x^2y^2-\left(2x+y\right)^2\)

\(=\left(2x+y+2xy\right)\left(2xy-2x+y\right)\)

Mấy cái còn lại nhân tung ra là được mà :))))

làm luôn đi cậu

a: \(=\dfrac{3x+6-2x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{x+10}{x^2-4}\)

b: \(=\dfrac{10x+15+4x-6+2x+5}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{16x+14}{\left(2x-3\right)\left(2x+3\right)}\)

a: \(\left(4x^5-8x^3\right):\left(-2x^3\right)\)

\(=-4x^5:2x^3+8x^3:2x^3\)

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

b: \(\left(9x^3-12x^2+3x\right):\left(-3x\right)\)

\(=-\frac{9x^3}{3x}+\frac{12x^2}{3x}-\frac{3x}{3x}\)

\(=-3x^2+4x-1\)

c: \(\left(xy^2+4x^2y^3-3x^2y^4\right):\left(-\frac12x^2y^3\right)\)

\(=-xy^2:\frac12x^2y^3-4x^2y^3:\frac12x^2y^3+3x^2y^4:\frac12x^2y^3\)

\(=-\frac{2}{xy}-8+6y\)

d: \(\left\lbrack2\left(x-y\right)^3-7\left(y-x\right)^2-\left(y-x\right)\right\rbrack:\left(x-y\right)\)

\(=\left\lbrack2\left(x-y\right)^3-7\left(x-y\right)^2+\left(x-y\right)\right\rbrack:\left(x-y\right)\)

\(=\frac{2\left(x-y\right)^3}{x-y}-\frac{7\left(x-y\right)^2}{x-y}+\frac{\left(x-y\right)}{x-y}\)

\(=2\left(x-y\right)^2-7\left(x-y\right)+1\)

a>(8x^2y+10xy6^2-6xy):2xy=4xy+5y-3

b>(3x^2-4x).(2x-6)=6x^3-26x^2+24x

ĐKXĐ: \(\left\{{}\begin{matrix}3x\ne-y\\3x\ne y\end{matrix}\right.\)

a. \(\dfrac{x}{3x+y}+\dfrac{x}{3x-y}-\dfrac{2xy}{y^2-9x^2}\)

\(=\dfrac{x.\left(3x-y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{x.\left(3x+y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{2xy}{9x^2-y^2}\)

\(=\dfrac{x.\left(3x+y+3x-y\right)+2xy}{\left(3x-y\right).\left(3x+y\right)}\)

\(=\dfrac{6x^2+2xy}{\left(3x-y\right).\left(3x+y\right)}\)

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

\(=\dfrac{2x}{3x-y}\)

ĐKXĐ: \(\left\{{}\begin{matrix}x\ne0\\x\ne-5\end{matrix}\right.\)

b. \(\dfrac{4x+5}{x^2+5x}-\dfrac{3}{x+5}\)

\(=\dfrac{4x+5}{x.\left(x+5\right)}-\dfrac{3x}{x.\left(x+5\right)}\)

\(=\dfrac{x+5}{x.\left(x+5\right)}\)

\(=\dfrac{1}{x}\)