Question

Сократить дробь 5-√5/√10-√2

Answer 1

С решением, √10/2 это ответ

Answer 2

To simplify the given fraction, we'll rationalize the denominator. Rationalizing the denominator means getting rid of square roots in the denominator.

Given fraction: (5 - √5) / (√10 - √2)

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is (√10 + √2):

[(5 - √5) / (√10 - √2)] * [(√10 + √2) / (√10 + √2)]

Now, let's simplify the expression:

Numerator: (5 - √5) * (√10 + √2) = 5√10 + 5√2 - √5 * √10 - √5 * √2 = 5√10 + 5√2 - √50 - √10

Denominator: (√10 - √2) * (√10 + √2) = √10 * √10 + √10 * √2 - √2 * √10 - √2 * √2 = 10 + √20 - √20 - 2 = 8

So, the simplified fraction is:

(5√10 + 5√2 - √50 - √10) / 8

However, we can further simplify this fraction. Notice that 5√2 - √10 is the common factor between the terms in the numerator:

(5√10 + 5√2 - √50 - √10) / 8 = (5√2 - √10) + (√10 - √50) / 8 = (5√2 - √10) + √10(1 - √5) / 8

So, the final simplified fraction is:

(5√2 - √10) + √10(1 - √5) / 8