Simplify (1/(x+2))^2+7(1/(x+2))+6

Apply the product rule to ${\displaystyle \frac{1}{x+2}}$.

One to any power is one.

Combine ${\displaystyle 7}$ and ${\displaystyle \frac{1}{x+2}}$.

Multiply ${\displaystyle \frac{7}{x+2}}$ by ${\displaystyle \frac{x+2}{x+2}}$.

Multiply ${\displaystyle \frac{7}{x+2}}$ by ${\displaystyle \frac{x+2}{x+2}}$.

Write ${\displaystyle 6}$ as a fraction with denominator ${\displaystyle 1}$.

Multiply ${\displaystyle \frac{6}{1}}$ by ${\displaystyle \frac{{(x+2)}^2}{{(x+2)}^2}}$.

Multiply ${\displaystyle \frac{6}{1}}$ by ${\displaystyle \frac{{(x+2)}^2}{{(x+2)}^2}}$.

Raise ${\displaystyle x+2}$ to the power of ${\displaystyle 1}$.

Raise ${\displaystyle x+2}$ to the power of ${\displaystyle 1}$.

Use the power rule ${\displaystyle a^m{a}^n=a^{m+n}}$ to combine exponents.

Add ${\displaystyle 1}$ and ${\displaystyle 1}$.

Apply the distributive property.

Multiply ${\displaystyle 7}$ by ${\displaystyle 2}$.

Rewrite ${\displaystyle {(x+2)}^2}$ as ${\displaystyle (x+2)(x+2)}$.

Expand ${\displaystyle (x+2)(x+2)}$ using the FOIL Method.

Simplify and combine like terms.

Apply the distributive property.

Simplify.

Add ${\displaystyle 1}$ and ${\displaystyle 14}$.

Add ${\displaystyle 7x}$ and ${\displaystyle 24x}$.

Simplify the expression.

For a polynomial of the form ${\displaystyle a{x}^2+bx+c}$, rewrite the middle term as a sum of two terms whose product is ${\displaystyle a\cdot c=6\cdot 39=234}$ and whose sum is ${\displaystyle b=31}$.

Factor out the greatest common factor from each group.

Factor the polynomial by factoring out the greatest common factor, ${\displaystyle 6x+13}$.