Thực hiện phép tính: a) $\left(\dfrac{1}{2}a^2x^4+\dfrac{4}{3}ax^3-\dfrac{2}{3}ax^2\right):\left(-\dfrac{2}{3}ax^2\right)$ b)...

Hiếu Nguyễn Quang

a)

$\left(\frac{1}{2}a^2x^4+\frac{4}{3}ax^3-\frac{2}{3}ax^2\right):\left(-\frac{2}{3}ax^2\right)$

$=\left\lbrack\frac{1}{2}:\left(-\frac{2}{3}\right)\left(a^2:a\right)\left(x^4:x^2\right)\right\rbrack+\left\lbrack\frac{4}{3}:\left(-\frac{2}{3}\right)\left(a:a\right)\left(x^3:x^2\right)\right\rbrack-\left\lbrack\frac{2}{3}:\left(-\frac{2}{3}\right)\left(a:a\right)\left(x^2:x^2\right)\right\rbrack$

$=-\frac{3}{4}ax^2-2x+1$

b)

$4\left(\frac{3}{4}x-1\right)+\left(12x^2-3x\right):\left(-3x\right)-\left(2x-1\right)$

$=3x-4+\left(\frac{12x^2}{-3x}-\frac{3x}{-3x}\right)-2x+1$

$=3x-4-4x+1-2x+1$

$=\left(3x-4x-2x\right)+\left(-4+1+1\right)$

$=-3x-2$.