\(A=\frac{\sqrt{x}-1}{^{^2x-x}}:\left(\frac{1}{\sqrt{X}}-\frac{1}{\sqrt{X}+1}\right)\)rut gon a
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AH
Akai Haruma
Giáo viên
13 tháng 7 2020
Lời giải:
ĐKXĐ: \(x\geq 0; x\neq 1\)
Ta có:
\(A=\frac{x+\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+2)}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}=\frac{x+\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+2)}+\frac{\sqrt{x}+2}{(\sqrt{x}-1)(\sqrt{x}+2)}+\frac{\sqrt{x}-1}{(\sqrt{x}+2)(\sqrt{x}-1)}\)
\(=\frac{x+\sqrt{x}+1+\sqrt{x}+2+\sqrt{x}-1}{(\sqrt{x}-1)(\sqrt{x}+2)}=\frac{x+3\sqrt{x}+2}{(\sqrt{x}-1)(\sqrt{x}+2)}=\frac{(\sqrt{x}+1)(\sqrt{x}+2)}{(\sqrt{x}-1)(\sqrt{x}+2)}=\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
15 tháng 7 2020
=\(\frac{x-2+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}.\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}.\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}+1}{\sqrt{x}}\)
5 tháng 7 2020
a) Ta có: \(A=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)
\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{2\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2+5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{3\sqrt{x}}{\sqrt{x}+2}\)
8 tháng 10 2017
B=\(\left(\frac{2x+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\)\(-\frac{\sqrt{x}}{x+\sqrt{x}+1}\))\(\left(\frac{\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}{1+\sqrt{x}}-\sqrt{x}\right)\)=\(\left(\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\)\(\left(x-2\sqrt{x}+1\right)\)=\(\sqrt{x}-1\)
\(A=\frac{\sqrt{x}-1}{x^2-x}:\left(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{x}+1}\right)\)
\(A=\frac{\sqrt{x}-1}{x\left(x-1\right)}:\left(\frac{\sqrt{x}+1-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)
\(A=\frac{1}{x\left(\sqrt{x}+1\right)}:\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(A=\frac{1}{x\left(\sqrt{x}+1\right)}.\left(\sqrt{x}+1\right)\)
\(A=\frac{1}{x}\)
A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )
A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )\(A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )\)