From the given (x^4-2x^3-x)/(x(x+4))x4−2x3−xx(x+4)
We can reduce the degree of the dividend and the divisor
(x^4-2x^3-x)/(x(x+4))x4−2x3−xx(x+4)
factor the common monomial x
(x(x^3-2x^2-1))/(x(x+4))x(x3−2x2−1)x(x+4)
(cancelx(x^3-2x^2-1))/(cancelx(x+4))
(x^3-2x^2-1)/(x+4)
Perform long division
" " " " ""underline(x^2-6x+24" " " " " ")
x+4|~x^3-2x^2+0*x-1
"" " " " " underline(x^3+4x^2" " " " "" " " " "" " " " ")
" " " " " " " "-6x^2+0*x-1
" " " " " " " "underline(-6x^2-24x" " " " "" " " " ")
" " " " " " " " " " " " " " "24x-1
" " " " " " " " " " " " " " "underline(24x+96)
" " " " " " " " " " " " " " " " " " -97larrremainder
We write our answer this way
("Dividend")/("Divisor")="Quotient"+("Remainder")/("Divisor")
(x^4-2x^3-x)/(x(x+4))=x^2-6x+24-97/(x+4)
God bless....I hope the explanation is useful.
