To subtract the rational expressions \( \frac{x^2}{2x - 12} - \frac{18}{x - 6} \), we first need a common denominator.
- The first fraction can be rewritten as \( \frac{x^2}{2(x - 6)} \).
- The second fraction can be rewritten as \( \frac{18}{x - 6} \) (we need to express this with the common denominator as well).
Now we can rewrite the second fraction:
\[ \frac{18}{x - 6} = \frac{18 \cdot 2}{2(x - 6)} = \frac{36}{2(x - 6)} \]
Now we can perform the subtraction:
\[ \frac{x^2}{2(x - 6)} - \frac{36}{2(x - 6)} = \frac{x^2 - 36}{2(x - 6)} \]
We can simplify \( x^2 - 36 \) as it can be factored:
\[ x^2 - 36 = (x - 6)(x + 6) \]
Thus, we have:
\[ \frac{(x - 6)(x + 6)}{2(x - 6)} \]
Since \( x - 6 \) in the numerator and denominator can be canceled (as long as \( x \neq 6 \)), we get:
\[ \frac{x + 6}{2} \]
Thus, the simplified answer is:
\[ \frac{x + 6}{2} \]
From your responses, the correct option is:
\[ \text{Start Fraction x plus 6 over 2 End Fraction} \]
1 answer