Question

(3a)/(a ^ 2 + ab + b ^ 2) • до знаменника a ^ 3 - b ^ 3

Answer 1

Ответ:

Объяснение:

а³ - b³ = (a-b)(a²+ab+b²)

Надо домножить числитель и знаменатель на (a-b)

3a(a-b) / (a-b)(a²+ab+b²)

3a²-3ab / (a-b)(a²+ab+b²)

Answer 2

To simplify the expression (3a)/(a^2 + ab + b^2) ÷ (a^3 - b^3), we can start by factoring the denominator of the first fraction and the numerator of the second fraction.

The denominator of the first fraction, a^2 + ab + b^2, cannot be factored further, so we leave it as it is.

The numerator of the second fraction, a^3 - b^3, is a difference of cubes and can be factored using the formula:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Now, the expression becomes:

(3a)/(a^2 + ab + b^2) ÷ [(a - b)(a^2 + ab + b^2)]

Since the denominators are the same, we can simplify further by canceling out the common factors:

(3a)/(a^2 + ab + b^2) ÷ (a - b)

Now, we have simplified the expression to (3a)/(a - b).