Question

Find the restricted values of x for the following rational expression.

Answer 1

Given the following expression:

`\text{ }\frac{x^2\text{ + x + 6}}{x^2\text{ - x - 2}}`

Let's determine the restricted value of x by simplifying first the expression.

`\text{ }\frac{x^2\text{ + x + 6}}{x^2\text{ - x - 2}}\text{ = }\frac{x^2\text{ + x + 6}}{(x\text{ }+1)(x-2)}`

Since the numerator x^2 + x + 6 cannot be factored out, let's stay it as what it is.

What's important is for us to be able to factor our the denominator. Restricted values are values that cannot be equal to x because it will give you a denominator of 0.

Determining the restrictions, we get:

x + 1 = 0

x = -1

x - 2 = 0

x = 2

Therefore, the restrictions of the given expressions are bellow:

`\begin{gathered} \text{ x }\\e\text{ -1} \\ \text{ x }\\e\text{ 2} \end{gathered}`