If x + 1/x = 99, find the value of 100x/(2x² + 2 + 102x) is?

Question: If x + 1/x = 99, find the value of 100x/(2x² + 2 + 102x) is?

Solution:
x + 1/x = 99
(x² + 1)/x = 99
x² + 1 = 99x
2(x² + 1) = 99x × 2
2x² + 2 = 198x

100x/(2x² + 2 + 102x) = 100x/(198x + 102x)
= 100x/300x
= 1/3