Question

which of the following is equal to the rational expression when x doesnt equal 1 or 3 x^2-9/ (x-1)(x-3)

Answer 1

Given the rational expression:

`\begin{gathered} (x^2-9)/((x-1)(x-3)) \\ when\text{ x}\\e1\text{ or 3} \end{gathered}`

When the value of x is not 1 or 3, the above expression can be expressed as

`\begin{gathered} ((x-3)(x+3))/((x-1)(x-3)) \\ recall\text{ that} \\ x^2-9=x^2-3^2=(x-3)(x+3)---difference\text{ of squares} \\ thus,\text{ we have} \\ (\cancel(x-3)(x+3))/((x-1)\cancel(x-3)) \\ =(x+3)/(x-1) \end{gathered}`

Hence, we have

`(x+3)/(x-1)`

The correct option is B