Question

1. multiply.

\\(\frac{x + 3}{3} cdot \frac{15x}{x^2 - 9}\\)
\\(\frac{x + 3}{3} cdot \frac{15x}{x^2 - 9} = square\\) (simplify your answer. type your answer in factored form )

Explanation:

Step1: Factor the denominator

Notice that \(x^2 - 9\) is a difference of squares, so \(x^2 - 9=(x + 3)(x - 3)\).
The expression becomes \(\frac{x + 3}{3}\cdot\frac{15x}{(x + 3)(x - 3)}\).

Step2: Cancel common factors

Cancel out the common factor \((x + 3)\) in the numerator and denominator. Also, simplify \(\frac{15}{3}=5\).
After canceling, we have \(\frac{1}{1}\cdot\frac{5x}{(x - 3)}\).

Step3: Multiply the remaining factors

Multiplying the remaining factors gives \(\frac{5x}{x - 3}\).

Answer:

\(\frac{5x}{x - 3}\)