VTMO 2026 - Grade 9 - Semifinal - SET 04 - Self-study Question 25

Question 25

Let
$$A=\frac{\sqrt{x}+1}{\sqrt{x}+2}-\frac{\sqrt{x}-2}{\sqrt{x}-1}-\frac{3\sqrt{x}}{x+\sqrt{x}-2}.$$
Which interval of $x$ gives $-1/3\lt A\lt -1/4$?

$49\lt x\lt 100$
$1\lt x\lt 4$
$5\lt x\lt 8$
$121\lt x\lt 130$
$35\lt x\lt 48$