JAMB - Mathematics (1991 - No. 25)
Simplify \(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)
-2x - 2\(\sqrt{x (1 + x)}\)
1 + 2x + 2\(\sqrt{x (1 + x)}\)
\(\sqrt{x (1 + x)}\)
1 + 2x - 2\(\sqrt{x (1 + x)}\)
Giải thích
\(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)
= \((\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}) (\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} + \sqrt{x}})\)
= \(\frac{(1 + x) + \sqrt{x(1 + x)} + \sqrt{x(1 + x)} + x}{(1 + x) - x}\)
= \(\frac{1 + 2x + 2\sqrt{x(1 + x)}}{1}\)
= \(1 + 2x + 2\sqrt{x(1 + x)}\)