Cho biểu thức
P = x / ( √x +√y) (1-√y) - y/ (√x +√y) (√x + 1) -xy /(√x + 1)(1-√y)
Xin lỗi vì máy mình hỏng nên không gõ được công thức.
ĐKXĐ:...
$P=\frac{x}{(\sqrt{x}+\sqrt{y})(1-\sqrt{y})}-\frac{y}{(\sqrt{x}+\sqrt{y})(1+\sqrt{x})}-\frac{xy}{(\sqrt{x}+1)(1-\sqrt{y})}$
$=\frac{x(\sqrt{x}+1)-y(1-\sqrt{y})-xy(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{(x\sqrt{x}+y\sqrt{y})+(x-y)-xy(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)+(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})-xy(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}-xy)}{(\sqrt{x}+\sqrt{y})(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}-xy}{(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{\sqrt{x}(1+\sqrt{x})-\sqrt{y}(1+\sqrt{x})+y(1+\sqrt{x})(1-\sqrt{x})}{(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{[\sqrt{x}-\sqrt{y}+y(1-\sqrt{x})](\sqrt{x}+1)}{(1-\sqrt{y})(\sqrt{x}+1)}$
$=\frac{\sqrt{x}-\sqrt{y}+y(1-\sqrt{x})}{1-\sqrt{y}}$
$=\frac{\sqrt{x}(1-\sqrt{y})(1+\sqrt{y})-\sqrt{y}(1-\sqrt{y})}{1-\sqrt{y}}$
$=\sqrt{x}+\sqrt{xy}-\sqrt{y}$
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