Questions: Simplify the rational expression. If the rational expression cannot be simplified, so state. (x+6)/(x^2-x-42) Select the correct choice below and fill in any answer boxes in your choice. A. (x+6)/(x^2-x-42)= B. The expression cannot be simplified.

Solution Steps

To simplify the rational expression \( \frac{x+6}{x^{2}-x-42} \), we first factor the denominator \( x^{2}-x-42 \).

The factored form is: \[ x^{2}-x-42 = (x - 7)(x + 6) \]

Now we can rewrite the original expression using the factored form of the denominator: \[ \frac{x+6}{(x - 7)(x + 6)} \]

Next, we notice that \( x + 6 \) is a common factor in both the numerator and the denominator. We can cancel this common factor: \[ \frac{x+6}{(x - 7)(x + 6)} = \frac{1}{x - 7} \]

Final Answer