a) \(\dfrac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
= \(\dfrac{3x^3-3x^2-4x^2+4x+x-1}{2x^3-2x^2+x^2-x-3x+3}\)
= \(\dfrac{3x^2\left(x-1\right)-4x\left(x-1\right)+\left(x-1\right)}{2x^2\left(x-1\right)+x\left(x-1\right)-3\left(x-1\right)}\)
=\(\dfrac{\left(x-1\right)\left(3x^2-4x+1\right)}{\left(x-1\right)\left(2x^2-x-3\right)}\)
= \(\dfrac{3x^2-3x-x+1}{2x^2+2x-3x-3}\)
= \(\dfrac{3x\left(x-1\right)-\left(x-1\right)}{2x\left(x+1\right)-3\left(x+1\right)}\)
= \(\dfrac{\left(x-1\right)\left(3x-1\right)}{\left(x+1\right)\left(2x-3\right)}\)
Mình không chắc là đúng hoàn toàn nha!
b) \(\dfrac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)
= \(\dfrac{x^3-3x^2y+3xy^2-y^3-3x^2y-3xy^2+y^3}{x-6y}\)
= \(\dfrac{x^3-6x^2y}{x-6y}\)
= \(\dfrac{x^2\left(x-6y\right)}{x-6y}\)
= \(x^2\)