Which of the following is equal to the rational expression when x ≠ -3? (x^(2)-9 )/(x+3) A. x + 3 B. x - 3 C. (1)/(x-3) D. (x-3)/(x+3)

Question

Which of the following is equal to the rational expression when x ≠ -3?


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

A. x + 3
B. x - 3
C.
`(1)/(x-3)`
D.
`(x-3)/(x+3)`

Answer 1

Choice B is correct answer.

Explanation:

We have given a rational expression.

x²-9 / x+3

We have to simplify the given expression.

Applying difference formula on the numerator of the expression, we have

a²-b² = (a-b)(a+b)

x²-9 = (x-3)(x+3)

x²-9 / x+3 = (x-3)(x+3) / x+3

x²-9 / x+3 = x-3 which is the answer.

Answer 2

Option B (x - 3).

Explanation:

The given expression is
`(x^(2)-9 )/(x+3)` when x ≠ 3.

Here we know from the identity

(a² - b²) = (a - b)(a + b)

(x² - 9) = (x - 3)(x + 3)

Now the fraction is in factorized form

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

Therefore the given option B. (x - 3) is the correct answer.