Rational Expressions Quick Check

Question

5 of 55 of 5 Items
Question
Express in simplest form: 36x−216/x2−36 .(1 point)
Responses

20x
Start Fraction 20 over x End Fraction

6x
Start Fraction 6 over x End Fraction

36x+6
Start Fraction 36 over x plus 6 End Fraction

36x−6

Answer 1

To simplify the expression \(\frac{36x - 216}{x^2 - 36}\), we start by factoring both the numerator and the denominator.

1. Factoring the numerator: \[ 36x - 216 = 36(x - 6) \]

2. Factoring the denominator: \[ x^2 - 36 = (x - 6)(x + 6) \quad \text{(This is a difference of squares)} \]

Now, substituting the factored forms into the expression, we have: \[ \frac{36(x - 6)}{(x - 6)(x + 6)} \]

3. Canceling the common factor \((x - 6)\) (as long as \(x \neq 6\)): \[ \frac{36}{x + 6} \]

So, the expression in simplest form is: \[ \frac{36}{x + 6} \]

None of the provided options match this result. Thus, it seems there might be a discrepancy between the calculated answer and the provided choices. Would you like to recheck the problem or discuss this further?