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

b: \(\frac{-20x}{3y^2}:\frac{-4x^3}{5y}=\frac{-20x}{3y^2}\cdot\frac{5y}{-4x^3}=\frac{20\cdot5\cdot xy}{3y^2\cdot4x^3}=\frac{100xy}{12x^3y^2}=\frac{25}{3x^2y}\)

c: \(\frac{4x+12}{\left(x+4\right)^2}:\frac{3\left(x+3\right)}{x+4}\)

\(=\frac{4\left(x+3\right)}{\left(x+4\right)^2}\cdot\frac{x+4}{3\cdot\left(x+3\right)}\)

\(=\frac{4}{3\left(x+4\right)}\)

a: Sửa đề: \(\frac{3y}{28x^2}\cdot\frac{2x}{7y^4}\cdot49x^4y^3\)

\(=\frac{3y}{7y^4}\cdot\frac{2x}{28x^2}\cdot49x^4y^3\)

\(=\frac{3}{7y^3}\cdot\frac{1}{14x}\cdot49x^4y^3=\frac37\cdot\frac{1}{14}\cdot49\cdot\frac{x^4}{x}\cdot\frac{y^3}{y^3}=\frac37\cdot\frac72\cdot x^3=\frac32x^3\)

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

Câu 12: B

Câu 13: C

Câu 14: A

C12 B

C13 C

C14 A

ban chia đa thức 1 biến đã sắp xếp nha

ban chia đa thức 1 biến đã sắp xếp nha

b. (x + 2)(x² - 2x + 4)

= x³ - 2x² + 4x + 2x² - 4x + 8

= x³ + 8

c: \(\dfrac{4x^3-8x^2+13x-5}{2x-1}=\dfrac{4x^3-2x^2-6x^2+3x+10x-5}{2x-1}\)

=2x^2-3x+5

Ta có \(\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)

\(=\frac{\left(x-2\right)^2-\left(x+2\right)^2}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{x-2+x+2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{\left(x-2+x+2\right)\left(x-2-x-2\right)}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{2x}{\left(x+2\right)\left(x-2\right)}\)

\(\frac{-4.2x}{\left(x+2\right)^2\left(x-2\right)^2}.\frac{\left(x+2\right)\left(x-2\right)}{2x}=\frac{-4}{\left(x+2\right)\left(x-2\right)}\)