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

Solution:

Given the rational expression:

$\begin{gathered} \frac{x^2-9}{(x-1)(x-3)} \\ when\text{ x}\ne1\text{ or 3} \end{gathered}$

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

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

Hence, we have

$\frac{x+3}{x-1}$

The correct option is B