Which of the following is equal to the rational expression below when [tex] x \neq 7 [/tex]?

[tex]
\frac{x^2-49}{x-7}
[/tex]

A. [tex] \frac{x+7}{x-7} [/tex]

B. [tex] x+7 [/tex]

C. [tex] \frac{1}{x+7} [/tex]

D. [tex] x-7 [/tex]



Answer :

To determine which of the given choices is equal to the rational expression [tex]\(\frac{x^2 - 49}{x - 7}\)[/tex] when [tex]\(x \neq 7\)[/tex], let's follow these steps:

1. Factor the Numerator: Notice that the numerator [tex]\(x^2 - 49\)[/tex] is a difference of squares. We can factor it accordingly:

[tex]\[ x^2 - 49 = (x - 7)(x + 7) \][/tex]

2. Rewrite the Expression: Substitute the factored form of the numerator back into the expression:

[tex]\[ \frac{x^2 - 49}{x - 7} = \frac{(x - 7)(x + 7)}{x - 7} \][/tex]

3. Simplify the Expression: Since [tex]\(x \neq 7\)[/tex], the [tex]\(x - 7\)[/tex] terms in the numerator and the denominator are not zero and can be canceled out:

[tex]\[ \frac{(x - 7)(x + 7)}{x - 7} = x + 7 \][/tex]

Therefore, the rational expression [tex]\(\frac{x^2 - 49}{x - 7}\)[/tex] simplifies to [tex]\(x + 7\)[/tex] when [tex]\(x \neq 7\)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{B. \ x+7} \][/tex]