How to divide?

Question

#(x^5+x^4-8)/(x^3-4x)#

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Answer 1 · 2018-03-28T11:13:20

#x^2+x+4+(4x^2+16x-8)/(x(x+2)(x-2))#

Divide by polynomial long division...

#(x^5+x^4-8):(x^3-4x)=#
#color(red)(x^2)+(x^5color(blue)(-x^5+4x^3)+x^4-8):(x^3-4x)#

#(x^4+4x^3-8):(x^3-4x)=#
#color(red)(x)+(x^4color(blue)(-x^4+4x^2)+4x^3-8):(x^3-4x)#

#(4x^3+4x^2-8):(x^3-4x)=#
#color(red)(4)+(4x^3color(blue)(-4x^3+16x)+4x^2-8):(x^3-4x)#

So all in all:
#color(red)(x^2+x+4)+(4x^2+16x-8)/(x(x+2)(x-2))#