根式/通分母 問題

1.
x = 100 - 5000/(100-y)
x = [100(100-y) - 5000]/(100-y)
x = [10000-100y-5000]/(100-y)
x = [5000-100y]/(100-y)
x = 100(50-y)/(100-y)

2.
as above, (100-y) should be read as 1 whole item in this step
just like if the fraction is w/(5-2), you won't mutiply it by 5 or 2

3.
use (a+b)(a-b) = a^2 - b^2
1/[sqrt(3)-2]
= [sqrt(3)+2] / {[sqrt(3)-2][sqrt(3)+2]}
= [sqrt(3)+2] / {[sqrt(3)]^2 - 2^2]}
= [sqrt(3)+2] / {3 - 4}
= -[sqrt(3)+2]