Question

Which of the following is equal to the rational expression when x≠1 or 3

Answer 1

Given:

$\text{ The expression }\frac{x^2-9}{(x-1)(x-3)}$

Required:

Which of the following is equal to the rational expression when x≠1 or 3

Explanation:

We know the formula

$a^2-b^2=(a-b)(a+b)$

Now,

$\begin{gathered} =\frac{x^2-9}{(x-1)(x-3)} \\ \text{ We can also write it as} \\ =\frac{x^2-3^2}{(x-1)(x-3)} \\ =\frac{(x-3)(x+3)}{(x-1)(x-3_)} \\ =\frac{x+3}{x-1} \end{gathered}$

Answer:

Option A is correct.