Question

match the following items with their descriptions for simplifying the following rational expression: $\frac{x + 6}{x^{2}+12x + 36}$

1. determine common factor(s) to reduce $\frac{1}{x + 6}$
2. factor the polynomial $x + 6$ is common between numerator and denominator
3. write in simplest terms $\frac{x + 6}{(x + 6)(x + 6)}$

Explanation:

Step1: Factor the polynomial

The denominator $x^{2}+12x + 36$ is a perfect - square trinomial. Using the formula $(a + b)^2=a^{2}+2ab + b^{2}$, where $a = x$ and $b = 6$, we have $x^{2}+12x + 36=(x + 6)(x + 6)$. So the rational expression becomes $\frac{x + 6}{(x + 6)(x + 6)}$.

Step2: Determine common factor(s) to reduce

The common factor between the numerator and the denominator is $x + 6$.

Step3: Write in simplest terms

Dividing both the numerator and the denominator by $x + 6$, we get $\frac{1}{x + 6}$.

Answer:

1. $\frac{x + 6}{(x + 6)(x + 6)}$
2. $x + 6$ is common between numerator and denominator
3. $\frac{1}{x + 6}$