To determine the value of [tex]\( x \)[/tex] that makes the rational expression
[tex]\[
\frac{x+9}{3-x}
\][/tex]
undefined, we need to focus on the denominator of the expression. A rational expression is undefined when its denominator is equal to zero. Therefore, we need to find the value of [tex]\( x \)[/tex] that satisfies the equation:
[tex]\[
3 - x = 0
\][/tex]
To solve for [tex]\( x \)[/tex], follow these steps:
1. Start with the equation:
[tex]\[
3 - x = 0
\][/tex]
2. Add [tex]\( x \)[/tex] to both sides to isolate the constant on one side:
[tex]\[
3 = x
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that makes the denominator zero is [tex]\( x = 3 \)[/tex].
Therefore, the rational expression [tex]\(\frac{x+9}{3-x}\)[/tex] is undefined when [tex]\( x = 3 \)[/tex].
