a: \(\dfrac{\left(x+1\right)}{x^2+2x-3}=\dfrac{\left(x+1\right)}{\left(x+3\right)\cdot\left(x-1\right)}=\dfrac{\left(x+1\right)\left(x+2\right)\left(x+5\right)}{\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x+5\right)}\)

\(\dfrac{-2x}{x^2+7x+10}=\dfrac{-2x}{\left(x+2\right)\left(x+5\right)}=\dfrac{-2x\left(x+3\right)\left(x-1\right)}{\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x-1\right)}\)

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

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

c: \(\dfrac{x-2y}{2}=\dfrac{\left(x-2y\right)\left(x-xy\right)}{2\left(x-xy\right)}\)

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

A +B=  \(\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 7x^2y^3-6xy^{4^{ }}+5x^3y-1-x^3y-7x^2y^{3^{ }}+5-xy^4\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ =\left(7x^2y^3-7x^2y^3\right)+\left(-6xy^{4^{ }}-xy^4\right)+\left(5x^3y-x^3y\right)+\left(-1+5\right)\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ =7xy^4+4x^3y+4\)

Ta có: A+B

\(=7x^2y^3-6xy^4+5x^3y-1-x^3y-7x^2y^3+5-xy^4\)

\(=\left(7x^2y^3-7x^2y^3\right)-\left(6xy^4+xy^4\right)+\left(5x^3y-x^3y\right)+\left(5-1\right)\)

\(=-7xy^4+4x^3y+4\)

a: \(\dfrac{2x^4-x^3-x^2+7x-4}{x^2+x-1}\)

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

=2x^2-3x+4

b: \(=\dfrac{y}{x\left(2x-y\right)}+\dfrac{4x}{y\left(y-2x\right)}\)

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

c: \(=\dfrac{6\left(x+8\right)}{7\left(x-1\right)}\cdot\dfrac{\left(x-1\right)^2}{\left(x-8\right)\left(x+8\right)}=\dfrac{6\left(x-1\right)}{7\left(x-8\right)}\)

\(2A-B=\left(7x^2y^3-6xy^4+5x^3y-1\right).2-\left(-x^3y-7x^2y^3-xy^4\right)\)

=>\(2A-B=\left(14x^2y^3-12xy^4+10x^3-2\right)-\left(-x^3y-7x^2y^3+5-xy^4\right)\)

=>\(2A-B=\left(phá\right)ngoặc\)

=>\(2A-B=\left(14x^2y^3-7x^2y^3\right)+\left(10x^3y+x^3y\right)-12xy^4-xy^2+\left(-2+5\right)\)

=>\(2A-B=7x^2y^3+11x^3y-12xy^4-xy^2+3\)

học giỏi

mọi người trả lời giúp mình với mình cần gấp

1.

\(a,\left(-xy\right)\left(-2x^2y+3xy-7x\right)\)

\(=2x^3y^2-3x^2y^2+7x^2y\)

\(b,\left(\dfrac{1}{6}x^2y^2\right)\left(-0,3x^2y-0,4xy+1\right)\)

\(=-\dfrac{1}{20}x^4y^3-\dfrac{1}{15}x^3y^3+\dfrac{1}{6}x^2y^2\)

\(c,\left(x+y\right)\left(x^2+2xy+y^2\right)\)

\(=\left(x+y\right)^3\)

\(=x^3+3x^2y+3xy^2+y^3\)

\(d,\left(x-y\right)\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3\)

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

2.

\(a,\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(=x^3-y^3\)

\(b,\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=x^3+y^3\)

\(c,\left(4x-1\right)\left(6y+1\right)-3x\left(8y+\dfrac{4}{3}\right)\)

\(=24xy+4x-6y-1-24xy-4x\)

\(=\left(24xy-24xy\right)+\left(4x-4x\right)-6y-1\)

\(=-6y-1\)

#Toru

bài này là tính hay giải hệ hay tìm x;y phải có điều kiên chứ

Xin lỗi mọi ng đầu bài là thu gọn đa thức rồi tìm bậc của đa thức đó

3y (x² - xy) - 7x² (y + xy)

= 3x² y - 3xy² - 7x² y - 7x³ y

= (3x² y - 7x² y) - 3xy² - 7x³ y

= -4x² y - 3xy² - 7x³ y

= y (-4x² - 3xy - 7x³ )

Chúc bạn học tốt!

Bậc: 3.

 Thực hiện phép tính (10x^5y^2-6x^2y^5+8x^2y^5):(-2x^2y^2)