Answer:
(3u + 24) / (u + 9)
Explanation:
6u + 72 / 2u + 24 ÷ u² + 21u + 108 / u² + 20u + 96
We'll begin by factorising u² + 21u + 108 and u² + 20u + 96. This can be obtained as follow:
u² + 21u + 108
Multiply u² and 108. The result is 108u². Find the factors of 108u² such that their sum will result to 21u. The factors are 12u and 9u.
u² + 12u + 9u + 108
u(u + 12) + 9(u + 12)
(u + 9)(u + 12)
u² + 20u + 96
Multiply u² and 96. The result is 96u². Find the factors of 96u² such that their sum will result to 20u. The factors are 12u and 8u.
u² + 12u + 8u + 96
u(u + 12) + 8(u + 12)
(u + 8)(u + 12)
6u + 72 / 2u + 24 ÷ u² + 21u + 108 / u² + 20u + 96 =
6u + 72 / 2u + 24 ÷ (u + 9)(u + 12) / (u + 8)(u + 12) =
(6u + 72) / (2u + 24) × (u + 8)(u + 12) / (u + 9)(u + 12)
(6u + 72)(u + 8)(u + 12) / (2u + 24)(u + 9)(u + 12) =
(6u + 72)(u + 8) / (2u + 24)(u + 9) =
6(u + 12)(u + 8) / 2(u + 12)(u + 9) =
6(u + 8) / 2(u + 9) = 3(u + 8) / (u + 9)
= (3u + 24) / (u + 9)