use the work shown below to find the simplified product.\n$\frac{25x^{2}}{2x + 6}cdot\frac{2}{5x}$\n$\frac{25…

use the work shown below to find the simplified product.\n$\frac{25x^{2}}{2x + 6}cdot\frac{2}{5x}$\n$\frac{25x^{2}}{2(x + 3)}cdot\frac{2}{5x}$\nchoose the simplified product.\n$\frac{1}{x + 3}$\n$\frac{2}{x + 3}$\n$\frac{5x}{x + 3}$\n$\frac{10x}{x + 3}$\ndone

use the work shown below to find the simplified product.\n$\frac{25x^{2}}{2x + 6}cdot\frac{2}{5x}$\n$\frac{25x^{2}}{2(x + 3)}cdot\frac{2}{5x}$\nchoose the simplified product.\n$\frac{1}{x + 3}$\n$\frac{2}{x + 3}$\n$\frac{5x}{x + 3}$\n$\frac{10x}{x + 3}$\ndone

Answer

Explanation:

Step1: Factor the denominator

Factor (2x + 6) to (2(x + 3)). So the expression becomes (\frac{25x^{2}}{2(x + 3)}\cdot\frac{2}{5x}).

Step2: Multiply the numerators and denominators

Multiply the numerators (25x^{2}\times2 = 50x^{2}), and multiply the denominators (2(x + 3)\times5x=10x(x + 3)). The expression is (\frac{50x^{2}}{10x(x + 3)}).

Step3: Simplify the fraction

Cancel out the common factors. (\frac{50x^{2}}{10x(x + 3)}=\frac{5x}{x + 3}) (divide 50 by 10 to get 5, and (x^{2}\div x=x)).

Answer:

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