To simplify this expression, we can first expand out the terms:
(u+1)² = u² + 2u + 1(10u-10)² = 100u² - 200u + 100
Next, we can multiply the expanded terms:
(u² + 2u + 1)(100u² - 200u + 100) = 100u⁴ - 200u³ + 100u² + 200u³ - 400u² + 200u + 100u² - 200u + 100= 100u⁴ - 100u² + 100
To find the denominator, we need to expand the expression:
100 - 100u³ • 1 - u² = 100 - 100u³ - 100u² + 100u⁵
Now, we can put both parts together and simplify the expression:
(100u⁴ - 100u² + 100) / (100 - 100u³ - 100u² + 100u⁵)
To simplify this expression, we can first expand out the terms:
(u+1)² = u² + 2u + 1
(10u-10)² = 100u² - 200u + 100
Next, we can multiply the expanded terms:
(u² + 2u + 1)(100u² - 200u + 100) = 100u⁴ - 200u³ + 100u² + 200u³ - 400u² + 200u + 100u² - 200u + 100
= 100u⁴ - 100u² + 100
To find the denominator, we need to expand the expression:
100 - 100u³ • 1 - u² = 100 - 100u³ - 100u² + 100u⁵
Now, we can put both parts together and simplify the expression:
(100u⁴ - 100u² + 100) / (100 - 100u³ - 100u² + 100u⁵)