Question

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Answer 1

Answer:

$\frac{k+5}{k-2}$

Step-by-step explanation:

$\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }$

multiply numerator and denominator by k² to eliminate fractions

= $\frac{k^2-25}{k^2-7k+10}$ ← factor numerator and denominator

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k² - 25 ← is a difference of squares

= (k - 5)(k + 5)

k² - 7k + 10

= (k - 5)(k - 2)

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= $\frac{(k-5)(k+5)}{(k-5)(k-2)}$ ← cancel (x - 5) on numerator / denominator

= $\frac{k+5}{k-2}$