Question

Which of the following values of $x$ makes the rational expression below undefined?

$\frac{x+9}{3-x}$

• A. $-9$
• B. $3$
• C. $9$
• D. $0$

Answer 1

The correct option is B

$3$

Explanation for the correct option.

Checking for all the values of $x$

Option (B):

For $x=3$

$\begin{array}{rcl}\frac{x+9}{3-x}& =& \frac{3+9}{3-3}\\ & =& \frac{12}{0}\mathrm{or}\infty \end{array}$

The rational expression is undefined.

Thus, option (B) is correct.

Explanation for the incorrect options.

Option (A):

For $x=-9$

$\begin{array}{rcl}\frac{x+9}{3-x}& =& \frac{-9+9}{3-9}\\ & =& 0\end{array}$

The rational expression is defined.

Thus, option (A) is incorrect.

Option (C):

For $x=9$

$\begin{array}{rcl}\frac{x+9}{3-x}& =& \frac{9+9}{3-9}\\ & =& \frac{18}{-6}\\ & =& -3\end{array}$

The rational expression is defined.

Thus, option (C) is incorrect.

Option (D):

For $x=0$

$\begin{array}{rcl}\frac{x+9}{3-x}& =& \frac{0+9}{3-0}\\ & =& \frac{9}{3}\\ & =& 3\end{array}$

The rational expression is defined.

Thus, option (D) is incorrect.

Hence, option (C) is correct.