Chapter 11.1, Problem 41PPE

To determine

Simplify the expression $\frac{x^2-9}{x+3}$ and explain how we get the answer as x − 3.

Answer to Problem 41PPE

  $\frac{x^2-9}{x+3}=(x-3)$ is same.

Explanation of Solution

Given:

Is $\frac{x^2-9}{x+3}$ the same as x − 3? Explain.

Concept Used:

For simplifying the expression $\frac{x^2-9}{x+3}$ ,

We use the difference of square rule: $a^2-b^2=(a+b)(a-b)$ to find the factors of numerator.

Calculation:

Using the rule: $a^2-b^2=(a+b)(a-b)$ to find the factors of numerator.

Cancel the common factor (x + 3) from the numerator and denominator.

  $\frac{x^2-9}{x+3}=\frac{(x+3)(x-3)}{(x+3)}=(x-3)$

Thus, $\frac{x^2-9}{x+3}=(x-3)$ is same.