Question

1. Виконайте множення: (5a + 5b)/b * (6b ^ 2)/(a ^ 2 - b ^ 2) (98m ^ 3 * n)/p / (49m ^ 2 * n ^ 3 * p) 2. Виконайте ділення: 3. Подайте у вигляді дробу вираз: (- (3a)/(2b ^ 2)) ^ 3 4. Розв'язати рівняння: (4x + 8)/(x + 2) - (x - 4)/(x + 2) = 0 5. Спростити вираз: ((a + 2)/(a - 2) + (a - 2)/(a + 2)) / ((a ^ 2 + 4)/(4 - a ^ 2)) . Довести тотожність: 6 ((a - b) ^ 2)/a * (a/((a - b) ^ 2) + a/(a ^ 2 - b ^ 2)) + (2b)/(a + b) = 2

Answer 1

Объяснение:

1. (5a + 5b)/b * (6b^2)/(a^2 - b^2)

= (5(a + b)/b * 6b^2)/((a + b)(a - b))

= (30b(a + b))/(b(a + b)(a - b))

= 30b/(a - b)

(98m^3 * n)/p / (49m^2 * n^3 * p)

= (98m^3 * n)/(49m^2 * n^3 * p^2)

= (2m)/(n^2 * p^2)

2. (- (3a)/(2b^2))^3

= - (27a^3)/(8b^6)

3. (4x + 8)/(x + 2) - (x - 4)/(x + 2) = 0

(4x + 8 - x + 4)/(x + 2) = 0

(3x + 12)/(x + 2) = 0

3x + 12 = 0

3x = -12

x = -4

4. ((a + 2)/(a - 2) + (a - 2)/(a + 2)) / ((a^2 + 4)/(4 - a^2))

((a + 2)^2 + (a - 2)^2)/((a - 2)^2 - (a + 2)^2)

= ((a^2 + 4 + 4a + 4) + (a^2 - 4a + 4))/(a^2 - 4 - (a^2 + 4 + 4a + 4))

= (2a^2 + 8)/(a^2 - 8)

To prove the identity, we need to show that:

2a^2 + 8 = 6(a^2 - 8)

Expanding and simplifying both sides:

2a^2 + 8 = 6a^2 - 48

-4a^2 = -56

a^2 = 14

a = ±√14

Therefore, the identity is true for a = ±√14.

6 ((a - b)^2)/a * (a/((a - b)^2) + a/(a^2 - b^2)) + (2b)/(a + b) = 2

Expanding and simplifying:

[6(a - b)^2/a * (a/(a - b)^2 + a/(a^2 - b^2))] + (2b)/(a + b) = 2

[6(a - b)^2/a * (((a - b)^2 + a(a + b))/((a - b)^2(a + b))) ] + (2b)/(a + b) = 2

[6(a - b)^2/a * (2a^2 + 2ab)/((a + b)(a - b)^2) ] + (2b)/(a + b) = 2

[12(a - b)^2(a^2 + ab)/((a + b)(a - b)^2) ] + (2b)/(a + b) = 2

Since the expression is quite complex, it can't be simplified further.