Question
Rational Expressions Quick Check
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
Answers
GPT-4o mini
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?
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?