# How do you divide (x^2+x-1)/(2x + 4) using polynomial long division?

$\frac{{x}^{2} + x - 1}{2 x + 4} = \frac{1}{2} x - \frac{1}{2} + \frac{1}{2 x + 4}$

#### Explanation:

We divide polynomials just like we are dividing integers

" " " " " " " "underline(1/2x-1/2 " " " " "larr )the quotient
$2 x + 4 \text{ } \lceiling {x}^{2} + x - 1$
" " " " " " " "underline(x^2+2x" " " " " " ")
$\text{ " " " " " " " " } - x - 1$
" " " " " " " " " "underline(-x-2 " " " " ")
$\text{ " " " " " " " " " " " " "+1 larr "remainder}$

Our final answer will be written

$\frac{{x}^{2} + x - 1}{2 x + 4} = \frac{1}{2} x - \frac{1}{2} + \frac{1}{2 x + 4}$

God bless....I hope the explanation is useful.