Question

question 2 (multiple choice worth 5 points) (04.01r lc) simplify \\(\frac{15x^2 - 18}{6}\\). options: \\(15x + 3\\), \\(x + 3\\), \\(\frac{5x^2 - 18}{2}\\), \\(\frac{5x^2 - 6}{2}\\)

Explanation:

Step1: Factor out the GCD of numerator

The numerator is $15x^{2}-18$. The greatest common divisor (GCD) of 15 and 18 is 3. So we factor out 3 from the numerator: $15x^{2}-18 = 3(5x^{2}-6)$.

Step2: Simplify the fraction

Now we have the fraction $\frac{3(5x^{2}-6)}{6}$. We can simplify the fraction by dividing the numerator and the denominator by their GCD, which is 3. So $\frac{3(5x^{2}-6)\div3}{6\div3}=\frac{5x^{2}-6}{2}$.

Answer:

$\frac{5x^{2}-6}{2}$