Câu 3: Trang 28 sách phát triển năng lực toán lớp 9 tập 1Rút gọn các biểu thức sau:a...

{
"content1": {
"a": "$\frac{1}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}+1 = \frac{\sqrt{x}-1+\sqrt{x}+1+(\sqrt{x}+1)(\sqrt{x}-1)}{(\sqrt{x}+1)(\sqrt{x}-1)} = \\ \frac{2\sqrt{x}}{x-1}$"
},
"content2": {
"b": "$\frac{(2+\sqrt{3x})^{2}-(\sqrt{3x}+1)^{2}}{2\sqrt{3x}+3} = \\ \frac{4 + 4\sqrt{3x}+3x - (3x + 2\sqrt{3x} + 1)}{2\sqrt{3x}+3} = \\ \frac{x+2\sqrt{3x}+3}{2\sqrt{3x}+3} = 1$"
},
"content3": {
"c": "$\frac{1}{\sqrt{x}+2}-\frac{2}{\sqrt{x}-2}-\frac{\sqrt{x}}{4-x} = \\ \frac{1}{\sqrt{x}+2}-\frac{2}{\sqrt{x}-2}-\\ \frac{\sqrt{x}(\sqrt{x}+2)}{(\sqrt{x}+2)(\sqrt{x}-2)} = \\ -\frac{4}{x-4}$"
},
"content4": {
"d": "$\frac{\sqrt{x+\sqrt{2x-1}}}{\sqrt{2}} = \\ \frac{\sqrt{\frac{4x-1+2\sqrt{2x-1}}{2}}}{\sqrt{2}} = \\ \sqrt{\frac{4x-1+2\sqrt{2x-1}}{4}} = \\ \sqrt{x+\frac{1}{2}}$"
},
"content5": {
"e": "$\frac{\sqrt{a}}{\sqrt{a+1}-\sqrt{a}}+\frac{\sqrt{a}}{\sqrt{a+1}+\sqrt{a}} = \\ \frac{\sqrt{a}(\sqrt{a+1}+\sqrt{a})+\sqrt{a}(\sqrt{a+1}-\sqrt{a})}{(\sqrt{a+1}-\sqrt{a})(\sqrt{a+1}+\sqrt{a})} = \\ \frac{2\sqrt{a+1}}{1} = 2\sqrt{a+1}$"
},
"content6": {
"f": "$\frac{1}{x+\sqrt{1+x^{2}}}+\frac{1}{x-\sqrt{1+x^{2}}}+2x = \\ \frac{x-\sqrt{1+x^{2}}+x+\sqrt{1+x^{2}}+2x(x+\sqrt{1+x^{2}})(x-\sqrt{1+x^{2}})}{(x+\sqrt{1+x^{2}})(x-\sqrt{1+x^{2}})} = \\ \frac{2+2x\sqrt{1+x^{2}}}{x^{2}-1} = \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ = \\frac{2(1+x^{2})}{x^{2}-1} = \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ = \\frac{2x^{2}+2}{x^{2}-1} = 2$"
}
}