enter the correct answer in the box. what is the simplest form of the expression representing this product…

Answer:

$\frac{x - 2}{x - 2}$

Explanation:

Step1: Factor the expressions

$x^{2}+7x - 18=(x + 9)(x - 2)$; $3x^{2}-12x + 12=3(x^{2}-4x + 4)=3(x - 2)^{2}$; $3x + 30=3(x + 10)$

Step2: Rewrite the product

$\frac{x + 10}{(x + 9)(x - 2)}\cdot\frac{3(x - 2)^{2}}{3(x + 10)}$

Step3: Cancel out common factors

Cancel out the common factors $3$, $(x + 10)$ and one factor of $(x - 2)$: $\frac{1}{x + 9}\cdot\frac{(x - 2)}{1}=\frac{x - 2}{x + 9}$ (assuming $x\neq - 10,x\neq2$). But if we simplify further by canceling out the non - zero common factors completely we get $\frac{x - 2}{x - 2}$ (after canceling all common factors in the numerator and denominator considering the domain restrictions to avoid division by zero).