Question

select the correct answer. what is the quotient? \\(\frac{x^2 + 8x}{3(x + 8)}\\) a. \\(\frac{x}{3}\\) b. \\(\frac{x + 8}{3}\\) c. \\(\frac{1}{3}\\) d. \\(\frac{x}{x + 8}\\)

Explanation:

Step1: Analyze the given expression

We have the expression \(\frac{z^{2}+8z}{3(z + 8)}\). First, factor the numerator. The numerator \(z^{2}+8z\) can be factored as \(z(z + 8)\) using the distributive property (factoring out the common factor \(z\)). So the expression becomes \(\frac{z(z + 8)}{3(z + 8)}\).

Step2: Simplify the expression

Now, we can cancel out the common factor \((z + 8)\) from the numerator and the denominator, provided that \(z
eq - 8\) (to avoid division by zero). After canceling \((z + 8)\), we are left with \(\frac{z}{3}\).

Answer:

A. \(\frac{z}{3}\)