Chapter 11.1, Problem 4LC

To determine

The expressions are rational? Explain your reasoning.

Answer to Problem 4LC

Expressions $\text{a:}\frac{\sqrt{x}+2}{x^2+4};\text{b:}\frac{y}{y+1}$ both are rational.

Explanation of Solution

Given:

Concept Used:

Rational expression is in the form $\frac{\text{P}}{\text{Q}}$ , where $\text{Q}\ne 0$ , denominator cannot be zero in any rational expression.

Calculation:

Expressions $\text{a:}\frac{\sqrt{x}+2}{x^2+4};\text{b:}\frac{y}{y+1}$ both are rational, and in the form of $\frac{\text{P}}{\text{Q}}$

Thus, expressions $\text{a:}\frac{\sqrt{x}+2}{x^2+4};\text{b:}\frac{y}{y+1}$ both are rational