скоротіть рівняння (a ^ - 5 + b ^ - 5)/(a ^ - 6) / ((a ^ - 3 * b ^ - 5 + a ^ - 8)/(a ^ - 4))
Ответы
Ответ:
a^5
Объяснение:
Simplify the following:
(1/b^5 + 1/a^5)/(a^(-6) (1/(a^3 b^5) + 1/a^8)/(a^(-4)))
Multiply the numerator of (1/(a^3 b^5) + 1/a^8)/(a^(-4)) by the reciprocal of the denominator. (1/(a^3 b^5) + 1/a^8)/(a^(-4)) = (1/(a^3 b^5) + 1/a^8) a^4:
(1/b^5 + 1/a^5)/(a^(-6) (a^4 (1/(a^3 b^5) + 1/a^8)))
Multiply the numerator of (1/b^5 + 1/a^5)/(a^(-6)) by the reciprocal of the denominator. (1/b^5 + 1/a^5)/(a^(-6)) = (1/b^5 + 1/a^5) a^6:
((a^6 (1/b^5 + 1/a^5)))/(a^4 (1/(a^3 b^5) + 1/a^8))
Combine powers. ((1/b^5 + 1/a^5) a^6)/((1/(a^3 b^5) + 1/a^8) a^4) = ((1/b^5 + 1/a^5) a^(6 - 4))/(1/(a^3 b^5) + 1/a^8):
(a^(6 - 4) (1/b^5 + 1/a^5))/(1/(a^3 b^5) + 1/a^8)
6 - 4 = 2:
(a^2 (1/b^5 + 1/a^5))/(1/(a^3 b^5) + 1/a^8)
Put ach term in 1/(a^3 b^5) + 1/a^8 over the common denominator a^8 b^5: 1/(a^3 b^5) + 1/a^8 = a^5/(a^8 b^5) + b^5/(a^8 b^5):
(a^2 (1/b^5 + 1/a^5))/((a^5/(a^8 b^5) + b^5/(a^8 b^5)))
a^5/(a^8 b^5) + b^5/(a^8 b^5) = (b^5 + a^5)/(a^8 b^5):
(a^2 (1/b^5 + 1/a^5))/(((b^5 + a^5)/(a^8 b^5)))
Put each term in 1/b^5 + 1/a^5 over the common denominator a^5 b^5: 1/b^5 + 1/a^5 = a^5/(a^5 b^5) + b^5/(a^5 b^5):
a^2/((b^5 + a^5)/(a^8 b^5)) (a^5/(a^5 b^5) + b^5/(a^5 b^5))
a^5/(a^5 b^5) + b^5/(a^5 b^5) = (b^5 + a^5)/(a^5 b^5):
a^2/((b^5 + a^5)/(a^8 b^5)) ((b^5 + a^5)/(a^5 b^5))
Combine powers. ((b^5 + a^5) a^2)/(a^5 b^5) = ((b^5 + a^5) a^(2 - 5))/b^5:
((a^(2 - 5) (b^5 + a^5))/b^5)/((b^5 + a^5)/(a^8 b^5))
Multiply the numerator by the reciprocal of the denominator, ((a^(2 - 5) (b^5 + a^5))/b^5)/((b^5 + a^5)/(a^8 b^5)) = ((b^5 + a^5) a^(2 - 5))/b^5×(a^8 b^5)/(b^5 + a^5):
(a^(2 - 5) a^8 b^5 (b^5 + a^5))/(b^5 (b^5 + a^5))
2 - 5 = -3:
(a^(-3) a^8 b^5 (b^5 + a^5))/(b^5 (b^5 + a^5))
((b^5 + a^5) a^8 b^5)/(b^5 (b^5 + a^5) a^3) = (b^5 (b^5 + a^5))/(b^5 (b^5 + a^5))×a^8/a^3 = a^8/a^3:
a^8/a^3
Combine powers. a^8/a^3 = a^(8 - 3):
a^(8 - 3)
8 - 3 = 5:
Answer: |
| a^5