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)

a. x-3/x-1
b. x+3/x-1
c.x-1/x-3

Answer 1

Answer: x+3/x-1

Explanation:

Answer 2

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

Explanation:

Given expression is:

`(x^(2)-9 )/((x-1)(x-3))`

Let us factorize the numerator using the formula:

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

`((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,
`(x^(2)-9 )/((x-1)(x-3)) =(x+3)/(x-1)`