Question

Rewrite the rational expression

Answer 1

The answer is (D) ⇒ (
`x^(2)+x-1)+(-6)/(x+4)`

Explanation:

∵
`(x^(3)+5x^(2)+3x-10)/(x+4)=x^(2)+(x^(2)+3x-10 )/(x+4)`

∵
`(x^(2)+3x-10 )/(x+4)=x+(-x-10)/(x+4)`

∵
`(-x-10)/(x+4)=-1+(-6)/(x+4)`

∴ The answer is (x² + x - 1) + (-6)/(x + 4)

Answer 2

D.
`(x^2+x-1)+(-6)/(x+4)`

Explanation:

The given rational expression is

`(x^3+5x^2+3x-10)/(x+4)`

We obtain the quotient and remainder using synthetic division.

1 5 3 -10

-4| -4 -4 4

1 1 -1 -6

The quotient is
`x^3+x-1` and the remainder is -6.

The expression becomes;

`(x^3+5x^2+3x-10)/(x+4)=(x^2+x-1)+(-6)/(x+4)`