2 Сократите дробь: a) 3-√3; б) a-25. √6-√2 √a-5

a) Сократим дробь (3-√3)/(√6-√2):

(3-√3)/(√6-√2) = (3-√3)/(√(3*2)-√2) = (3-√3)/(√3*√2-√2) = (3-√3)/(√2(√3-1)) = (√3(√3-1))/(√2(√3-1)) = √3/√2 = (√3*√2)/(√2*√2) = √6/2

б) Сократим дробь (a-25)/(√a-5):

(a-25)/(√a-5) = ((√a)² - 5²)/(√a-5) = (√a-5)(√a+5)/(√a-5) = √a+5

Ответ: а) √6/2; б) √a+5