Question

Which of the following is equal to the rational expression when x does not equal 3 or 1 x^2-9/(x-1)(x-3)

Answer 1

Answer:

b.  $\frac{x+3}{x-1}$

Step-by-step explanation:

Given expression is:

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

Let us factorize the numerator using the formula:

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

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

Since x ≠ 3, let us cancel the common factor x - 3 in the numerator and in the denominator.

So, $\frac{x^{2}-9 }{(x-1)(x-3)} =\frac{x+3}{x-1}$