)) Simplify Write your answer using whole numbers and variables. (g-7)/(g^2)-2g-35 square

To simplify the expression \(\frac{g-7}{g^2 - 2g - 35}\), we need to factor the denominator.<br /><br />First, let's factor the quadratic expression in the denominator:<br />\[ g^2 - 2g - 35 \]<br /><br />We look for two numbers that multiply to \(-35\) and add up to \(-2\). These numbers are \(5\) and \(-7\), because:<br />\[ 5 \times (-7) = -35 \]<br />\[ 5 + (-7) = -2 \]<br /><br />So, we can factor the quadratic as:<br />\[ g^2 - 2g - 35 = (g - 7)(g + 5) \]<br /><br />Now, we rewrite the original expression using this factorization:<br />\[ \frac{g-7}{(g-7)(g+5)} \]<br /><br />Next, we can cancel the common factor \((g-7)\) in the numerator and the denominator:<br />\[ \frac{g-7}{(g-7)(g+5)} = \frac{1}{g+5} \quad \text{(for } g \neq 7 \text{)} \]<br /><br />Thus, the simplified form of the given expression is:<br />\[ \boxed{\frac{1}{g+5}} \]