Given: #(color(blue)(-x^4-3x^3-2x^2-2x+3))/(color(green)(x^2+3)#
Note that I use place keepers that have no value. This is to assist with formatting. Example #0x^3#
#color(white)("dddddddddddddddd")color(blue)(-x^4-3x^3-2x^2-2x+3)#
#color(magenta)(-(x^2))color(green)((x^2+3))-> color(white)(".d")ul(-x^4+0x^3-3x^2 larr" Subtract")#
#color(white)("ddddddddddddddddddd") 0-3x^3+color(white)(".")x^2-2x+3#
#color(magenta)(-3x)color(green)((x^2+3))->color(white)("ddddddd")-ul(3x^3+0x^2-9x larr" Subtract")#
#color(white)("dddddddddddddddddddddddd")0 +x^2color(white)("d")+7x+3#
#color(magenta)(+1)color(green)((x^2+3))->color(white)("ddddddddddddddd")ul(x^2color(white)("d")+0x+3 larr" Sub.")#
#color(white)("ddddddddddd")color(magenta)("Remainder"->color(white)("dddddd")0color(white)("d")color(magenta)(+7x+0)#
#color(magenta)(-x^2-3x+1+(7x)/(color(green)(x^2+3))#
