Question

rationalize the denominator. Assume that all expressions under raticals represent positive numbers
(√(c)-√(d))/(√(c)+√(d))

Answer 1

to rationalize these fraction, just multiply the conjugate
(√(c)-√(d))/(√(c)+√(d))
=(√(c)-√(d))/(√(c)+√(d)) x (√(c)-√(d))/(√(c)-√(d))
=(√(c)-√(d))^2 /[(√(c)+√(d)) (√(c)-√(d))]
= (√(c)-√(d))^2/(c-d)

note that
[(√(c)+√(d)) (√(c)-√(d))] can be written as (√(c)^2-√(d)^2) = c-d