Question

A rational expression has been simplified below,(x + 4)(x-2).x+49(x - 2) 9For what values of x are the two expressions equal?A. All real numbers except 2B. All real numbers except -4 and 2C. All real numbers except -4D. All real numbers

Answer 1

Answer: A. All real numbers except 2.

Step by step solution:

$\frac{(x+4)(x-2)}{9(x-2)}=\frac{x+4}{9}$

The expressions are equal for the set of values of x in which the functions are defined, we need to determine the domain of the rational expression before it is simplified.

$\frac{(x+4)(x-2)}{9(x-2)}$

In a rational expression, the denominator can not be 0, then the domain is:

$\begin{gathered} 9(x-2)\ne0 \\ x-2\ne0 \\ x\ne2 \end{gathered}$

All real numbers except 2. For the expression to be defined x can not be 2.