1)) Simplify.Write your answer using whole numbers and variables. (n+17)/(n^2)+19n+34 square

To simplify the expression \(\frac{n+17}{n^2 + 19n + 34}\), we need to factor the denominator.<br /><br />First, let's factor the quadratic expression in the denominator:<br />\[ n^2 + 19n + 34 \]<br /><br />We look for two numbers that multiply to 34 and add up to 19. These numbers are 2 and 17 because:<br />\[ 2 \times 17 = 34 \]<br />\[ 2 + 17 = 19 \]<br /><br />So, we can factor the quadratic as:<br />\[ n^2 + 19n + 34 = (n + 2)(n + 17) \]<br /><br />Now, we rewrite the original expression using this factorization:<br />\[ \frac{n+17}{(n+2)(n+17)} \]<br /><br />Next, we can cancel the common factor \((n + 17)\) in the numerator and the denominator:<br />\[ \frac{n+17}{(n+2)(n+17)} = \frac{1}{n+2} \]<br /><br />Thus, the simplified form of the given expression is:<br />\[ \boxed{\frac{1}{n+2}} \]