Chapter 14.3, Problem 84AYU

To determine

To find: The graph of $R\left(x\right)$.

Answer to Problem 84AYU

Explanation of Solution

Given:

$R\left(x\right) = \frac{x^3 + x^2 + 3x + 3}{x^4 + x^3 + 2x + 2}$

Calculation:

$R\left(x\right) = \frac{x^3 + x^2 + 3x + 3}{x^4 + x^3 + 2x + 2}$

$R\left(x\right) = \frac{\left(x^2 + 3\right)\left(x + 1\right)}{\left(x^3 + 2\right)\left(x + 1\right)}$

$R\left(x\right) = \frac{x^2 + 3}{x^3 + 2}$

Graph of $R$ is as follows: