Find the Excluded Values 9/(x+6)
The problem is asking you to identify the excluded value(s) in the given mathematical expression, which is 9/(x+6). To determine the excluded value(s), you would have to find any value(s) of x that would make the denominator (x+6) in this case equal to zero, because division by zero is undefined in mathematics. Hence, the excluded value(s) are the specific number(s) that are not permitted for x, since they would result in an invalid expression.
$\frac{9}{\left(\right. x + 6 \left.\right)}$
Answer
Solution:
Determine the Non-permissible Values for $\frac{9}{x + 6}$
Step 1: Identify the values of $x$ that will make the denominator zero, since division by zero is undefined. Solve the equation $x + 6 = 0$.
Step 2: Isolate $x$ by subtracting $6$ from both sides, resulting in $x = -6$.
Step 3: The value $x = -6$ is the excluded value for the expression $\frac{9}{x + 6}$, as it would make the denominator zero.
Knowledge Notes:
To determine the excluded values for a rational expression, you need to identify the values for the variable that would make the denominator equal to zero. A rational expression is undefined when its denominator is zero because division by zero is not allowed in mathematics.
Here are the relevant knowledge points:
Rational Expressions: A rational expression is a fraction in which both the numerator and the denominator are polynomials. The expression $\frac{9}{x + 6}$ is a rational expression.
Undefined Expressions: A mathematical expression is considered undefined if it involves operations that are not mathematically valid, such as division by zero.
Solving Linear Equations: To find the value of $x$ that makes the denominator zero, you need to solve a linear equation. In this case, the linear equation is $x + 6 = 0$.
Excluded Values: In the context of rational expressions, excluded values are specific values of the variable that make the denominator zero. These values are not part of the domain of the expression.
Isolating the Variable: To solve for $x$, you perform algebraic operations to isolate the variable on one side of the equation. In this problem, subtracting $6$ from both sides of the equation $x + 6 = 0$ isolates $x$.
By understanding these concepts, you can determine the excluded values for any rational expression and ensure that the expression remains defined for all other values of the variable.
