Đáp án:
\(\frac{(\sqrt{x}+1)^{2}}{\sqrt{x}(\sqrt{x}+2)}\)
Giải thích các bước giải:
\(\frac{x-1}{\sqrt{x}}:(\frac{x-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}})\)
=\(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}}:(\frac{x-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{\sqrt{x}(\sqrt{x}+1)})\)
=\(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}}:(\frac{(\sqrt{x}-1)(\sqrt{x}+1)(\sqrt{x}+1)-(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}+1)}\)
=\(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}}:(\frac{(\sqrt{x}-1)(\sqrt{x}+1)^{2}-1}{\sqrt{x}(\sqrt{x}+1)})\)
=\(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}}:(\frac{(\sqrt{x}-1)\sqrt{x}(\sqrt{x}+2)}{\sqrt{x}(\sqrt{x}+1)}\)
=\(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}}\cdot \frac{\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+2)}\)
=\(\frac{(\sqrt{x}+1)^{2}}{\sqrt{x}(\sqrt{x}+2)}\)
