Question

Сократите дробь (a-4√a+16)/(a√a+64)

Answer 1

Решение задания приложено

Answer 2

(a- 4√a+16)          (√²a- 4√a+4²)        (√²a- 4√a+4²)                       1
-------------------- = ---------------------- = ------------------------------ = ----------------
(a√a+64)            (√а)³+4³               (√а+4) (√²a- 4√a+4²)          (√а+4)

Answer 3

To simplify the given fraction, we can follow these steps:

Step 1: Factorize the denominators. Step 2: Cancel out common factors between the numerator and denominator. Step 3: Simplify the remaining expression.

Given fraction: (a - 4√a + 16) / (a√a + 64)

Step 1: Factorize the denominators. The denominator (a√a + 64) cannot be simplified further, as it is already in its simplest form.

Step 2: Cancel out common factors between the numerator and denominator. The numerator (a - 4√a + 16) can be factored as follows: a - 4√a + 16 = (a - 4√a + 4√a - 16) = (a - 4√a) + (4√a - 16) = √a(a - 4) + 4(√a - 4)

Step 3: Simplify the remaining expression. Now, the fraction becomes:

(√a(a - 4) + 4(√a - 4)) / (a√a + 64)

We can further factor out (√a - 4) from the numerator:

(√a(a - 4) + 4(√a - 4)) = (√a - 4)(√a + 4)

The simplified fraction is:

(√a - 4)(√a + 4) / (a√a + 64)