Question

find the difference.
\\(\dfrac{k}{k^2 - 9k + 20} - \dfrac{5}{k^2 - 9k + 20}\\)
\\(\bigcirc\\) a. \\(\dfrac{k - 5}{k - 4}\\)
\\(\bigcirc\\) b. \\(\dfrac{1}{k + 4}\\)
\\(\bigcirc\\) c. \\(\dfrac{1}{k - 4}\\)
\\(\bigcirc\\) d. \\(\dfrac{k - 5}{0}\\)

Explanation:

Step1: Subtract the numerators

Since the denominators are the same ($k^2 - 9k + 20$), we subtract the numerators: $\frac{k - 5}{k^2 - 9k + 20}$.

Step2: Factor the denominator

Factor $k^2 - 9k + 20$: $k^2 - 9k + 20=(k - 4)(k - 5)$.

Step3: Simplify the fraction

Substitute the factored form into the fraction: $\frac{k - 5}{(k - 4)(k - 5)}$. Cancel out the common factor $(k - 5)$ (assuming $k
eq5$), we get $\frac{1}{k - 4}$.

Answer:

C. $\frac{1}{k - 4}$