Question

drag the tiles to the correct boxes. not all tiles will be used.

determine which steps are used to find the product shown. put the steps in the order in which they would be performed.

\\\frac{x^2 + 7x + 10}{x^2 + 4x + 4} \cdot \frac{x^2 + 3x + 2}{x^2 + 6x + 5}\\

\\\frac{(x+2)(x+5)}{(x+2)(x+2)} \cdot \frac{(x+1)(x+2)}{(x+5)(x+1)}\\

\\\frac{(x+5)(x+2)}{(x+2)(x+5)}\\

\\\frac{(x+5)(x+2)}{(x+5)}\\

\\x+2\\

\\\frac{(x+7)(x+1)}{(x+4)(x+2)}\\

\\1\\

\\\frac{(x+7)(x+1)}{(x+4)(x+1)} \cdot \frac{(x+3)(x+1)}{(x+3)(x+2)}\\

\\\frac{(x+5)}{(x+2)} \cdot \frac{(x+2)}{(x+5)}\\

Explanation:

Factor the numerators and denominators of the given expression

$$ \frac{x^2 + 7x + 10}{x^2 + 4x + 4} \cdot \frac{x^2 + 3x + 2}{x^2 + 6x + 5} = \frac{(x+2)(x+5)}{(x+2)(x+2)} \cdot \frac{(x+1)(x+2)}{(x+5)(x+1)} $$

Multiply the rational expressions and group common factors

$$ \frac{(x+2)(x+5)(x+1)(x+2)}{(x+2)(x+2)(x+5)(x+1)} = \frac{(x+5)(x+2)}{(x+2)(x+5)} $$

Simplify the remaining common factors to find the final product

$$ \frac{(x+5)(x+2)}{(x+2)(x+5)} = 1 $$

Answer:

Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.

$$\frac{x^2 + 7x + 10}{x^2 + 4x + 4} \cdot \frac{x^2 + 3x + 2}{x^2 + 6x + 5}$$

Step 1:
<blank>\(\frac{(x + 2)(x + 5)}{(x + 2)(x + 2)} \cdot \frac{(x + 1)(x + 2)}{(x + 5)(x + 1)}\)</blank>

Step 2:
<blank>\(\frac{(x + 5)(x + 2)}{(x + 2)(x + 5)}\)</blank>

Step 3:
<blank>\(\frac{(x + 5)(x + 2)}{(x + 5)}\)</blank>

Step 4:
<blank>\(1\)</blank>