Question

Divide and simplify as much as possible: -20v^7 x^7 + 12v^4 x^7 / 4v^5 x^4

Answer 1

$\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{-20v^7x^7}{4v^5x^4}+\dfrac{12v^4x^7}{4v^5x^4}=-5v^{7-5}x^{7-4}+3v^{4-5}x^{7-4}\\\\=\boxed{3v^{-1}x^3-5v^2x^3}$

Used

$\dfrac{a^n}{a^m}=a^{n-m}$

Other method:

$\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{4v^4x^4(-5v^3x^3+3x^3)}{4v^4x^4(v)}=\dfrac{3x^3-5v^3x^3}{v}$