1)) Simplify.Write your answer using whole numbers and variables. (k^2-8k+15)/(k-3) square

To simplify the expression \(\frac{k^2 - 8k + 15}{k - 3}\), we need to factor the numerator and then simplify the fraction.<br /><br />First, let's factor the quadratic expression in the numerator:<br />\[ k^2 - 8k + 15 \]<br /><br />We need to find two numbers that multiply to 15 and add up to -8. These numbers are -3 and -5 because:<br />\[ (-3) \times (-5) = 15 \]<br />\[ (-3) + (-5) = -8 \]<br /><br />So, we can factor the quadratic as:<br />\[ k^2 - 8k + 15 = (k - 3)(k - 5) \]<br /><br />Now, substitute this factored form back into the original expression:<br />\[ \frac{k^2 - 8k + 15}{k - 3} = \frac{(k - 3)(k - 5)}{k - 3} \]<br /><br />Next, we can cancel the common factor \((k - 3)\) in the numerator and the denominator:<br />\[ \frac{(k - 3)(k - 5)}{k - 3} = k - 5 \quad \text{(for } k \neq 3\text{)} \]<br /><br />Therefore, the simplified form of the given expression is:<br />\[ \boxed{k - 5} \]