Question

(9a^2+4y^2)/(3a-2y)+12ay/(2y-3a)

Answer 1

Решение смотри внизу

Answer 2

To simplify the expression (9a^2 + 4y^2)/(3a - 2y) + 12ay/(2y - 3a), we need to find a common denominator for both fractions and then combine them.

Step 1: Find the common denominator. The common denominator for (3a - 2y) and (2y - 3a) is (3a - 2y)(2y - 3a).

Step 2: Convert each fraction to have the common denominator. For the first fraction (9a^2 + 4y^2)/(3a - 2y), we need to multiply both the numerator and the denominator by (2y - 3a): [(9a^2 + 4y^2)(2y - 3a)] / [(3a - 2y)(2y - 3a)]

For the second fraction 12ay/(2y - 3a), we need to multiply both the numerator and the denominator by (3a - 2y): [12ay(3a - 2y)] / [(2y - 3a)(3a - 2y)]

Step 3: Combine the fractions. Now that both fractions have the same denominator, we can add them together: [(9a^2 + 4y^2)(2y - 3a) + 12ay(3a - 2y)] / [(3a - 2y)(2y - 3a)]

Step 4: Expand and simplify. Let's expand the numerator: (18a^2y - 27a^3 + 8y^3 + 36a^2y - 24ay^2) / [(3a - 2y)(2y - 3a)]

Combine like terms in the numerator: (54a^2y + 8y^3 - 27a^3 - 24ay^2) / [(3a - 2y)(2y - 3a)]

The simplified expression is: (54a^2y + 8y^3 - 27a^3 - 24ay^2) / [(3a - 2y)(2y - 3a)]