(√(x) +1)/(x-√(x) +1) Với x≥0. Tìm GTLN

Question

`(√(x) +1)/(x-√(x) +1)` Với x≥0. Tìm GTLN

Answer 1

Explanation:

`(√(x)+1 )/(x-√(x)+1 )=(√(x)+1)/((x+1)-√(x))\\\\=((√(x)+1)([x+1]+√(x)))/(([x+1]-√(x))+([x+1)+√(x)]))\\\\=(√(x)*x+√(x)*1+√(x)*√(x)+1*x+1*1+1*√(x))/((x+1)^(2)-(√(x))^(2))\\\\\\=(x√(x)+√(x)+x+1+x+√(x))/(x^(2)+2x+1-x)\\\\=(x√(x)+2√(x)+2x+1)/(x^(2)+x+1)\\\\`