Answer:
[tex]\frac{k+5}{k-2}[/tex]
Step-by-step explanation:
[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]
multiply numerator and denominator by k² to eliminate fractions
= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← 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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= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator
= [tex]\frac{k+5}{k-2}[/tex]