Question

How do you divide `( x^4-2x^3-x)/(x(x+4))`?

Answer 1

`(x^4-2x^3-x)/(x(x+4))=(x^3-2x^2-1)/(x+4)=color(red)(x^2-6x+24-97/(x+4))`

Explanation:

From the given `(x^4-2x^3-x)/(x(x+4))`

We can reduce the degree of the dividend and the divisor

`(x^4-2x^3-x)/(x(x+4))`

factor the common monomial x

`(x(x^3-2x^2-1))/(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)`
`" " " " " " " " " " " " " " " " " " -97` `larr`remainder

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.