# The area of a rectangle is 2r^2+r-1. The length is r+1. What simplified expression represents the width?

Mar 4, 2018

$w i \mathrm{dt} h = 2 r - 1$

#### Explanation:

I would use synthetic division to divide $2 {r}^{2} + r - 1$ by $r + 1$. The quotient is $2 r - 1$.

In other words,

$A = l \cdot w$

$\frac{A}{l} = w$

$\frac{2 {r}^{2} + r - 1}{r + 1} = 2 r - 1$