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28 tháng 3 2018
\(A=\left(\frac{2+\sqrt{x}}{x-5\sqrt{x}+6}-\frac{\sqrt{x}+3}{2-\sqrt{x}}-\frac{\sqrt{x}+2}{\sqrt{x}-3}\right)\) \(:\left(2-\frac{\sqrt{x}}{\sqrt{x}+1}\right)\)
\(A=\left[\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+2}{\sqrt{x}-3}\right]\)
\(:\left[\frac{2\left(\sqrt{x}+1\right)-\sqrt{x}}{\sqrt{x}+1}\right]\)
\(A=\left[\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\frac{x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+2}{\sqrt{x}-3}\right]\)
\(:\left[\frac{2\sqrt{x}+2-\sqrt{x}}{\sqrt{x}+1}\right]\)
\(A=\left[\frac{\sqrt{x}+2+x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\right]\) \(:\left[\frac{\sqrt{x}+2}{\sqrt{x}+1}\right]\)
\(A=\left[\frac{\sqrt{x}+x-7-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right]:\frac{\sqrt{x}+2}{\sqrt{x}+1}\)
\(A=\frac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\frac{\sqrt{x}+2}{\sqrt{x}+1}\)
\(A=\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
TT
3
21 tháng 11 2017
Cái này dễ mà bn
Ta có:\(A=\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\left(ĐK:x\ne2;-3\right)\)
\(\Leftrightarrow A=\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}\)
\(\Leftrightarrow A=\frac{x^2-4-5-x-3}{\left(x+3\right)\left(x-2\right)}\)
\(\Leftrightarrow A=\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}=\frac{x+4}{x-2}\)
20 tháng 6 2017
Đặt \(\hept{\begin{cases}\left(x+\frac{1}{x}\right)^3=a\\x^3+\frac{1}{x^3}=b\end{cases}}\)
Ta có
\(A=\frac{\left(x+\frac{1}{x}\right)^6-\left(x^6+2+\frac{1}{x^6}\right)}{\left(x+\frac{1}{x}\right)^3+x^3+\frac{1}{x^3}}=\frac{\left(x+\frac{1}{x}\right)^6-\left(x^3+\frac{1}{x^3}\right)^2}{\left(x+\frac{1}{x}\right)^3+x^3+\frac{1}{x^3}}\)
\(=\frac{a^2-b^2}{a+b}=a-b\)
\(=\left(x+\frac{1}{x}\right)^3-\left(x^3+\frac{1}{x^3}\right)\)
\(=x^3+3\left(x+\frac{1}{x}\right)+\frac{1}{x^3}-\left(x^3+\frac{1}{x^3}\right)=\frac{3x^2+3}{x}\)
NN
1
N
23 tháng 12 2018
ĐKXĐ: x khác 2 và -3
\(P=\frac{x+2}{x+3}-\frac{5}{x+2x-3x-6}-\frac{1}{x-2}\)
\(P=\frac{\left(x+2\right).\left(x-2\right)}{\left(x+3\right).\left(x-2\right)}-\frac{5}{\left(x-2\right).\left(x+3\right)}-\frac{x+3}{\left(x-2\right).\left(x+3\right)}\)
\(P=\frac{x^2-4-5-x-3}{\left(x-2\right).\left(x+3\right)}=\frac{x^2-x-12}{\left(x+2\right).\left(x+3\right)}=\frac{\left(x-4\right).\left(x+3\right)}{\left(x+2\right).\left(x+3\right)}=\frac{x-4}{x+2}\)
23 tháng 10 2020
\(C=\left(1-\frac{x}{x+1}\right)\div\left(\frac{x+3}{x-2}+\frac{2+x}{3-x}+\frac{x+2}{x^2-5x+6}\right)\)
ĐKXĐ : x ≠ -1 ; x ≠ 2 ; x ≠ 3 ; x ≠ 11/5
\(=\left(\frac{x+1}{x+1}-\frac{x}{x+1}\right)\div\left(\frac{x+3}{x-2}-\frac{x+2}{x-3}+\frac{x+2}{\left(x-2\right)\left(x-3\right)}\right)\)
\(=\frac{1}{x+1}\div\left(\frac{\left(x+3\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}-\frac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}+\frac{x+2}{\left(x-2\right)\left(x-3\right)}\right)\)
\(=\frac{1}{x+1}\div\left(\frac{x^2-9}{\left(x-2\right)\left(x-3\right)}-\frac{x^2-4}{\left(x-2\right)\left(x-3\right)}+\frac{x+2}{\left(x-2\right)\left(x-3\right)}\right)\)
\(=\frac{1}{x+1}\div\left(\frac{x^2-9-x^2+4+x+2}{\left(x-2\right)\left(x-3\right)}\right)\)
\(=\frac{1}{x+1}\div\frac{x-3}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{1}{x+1}\times\frac{x-2}{1}\)
\(=\frac{x-2}{x+1}\)
8 tháng 7 2018
\(A=\left(\frac{x-2}{x+2}-\frac{x+2}{2-x}-\frac{x^2-3x+6}{x^2-4}\right):\left(1-\frac{3}{x-2}\right)\)
\(=\left(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}+\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x^2-3x+6}{\left(x-2\right)\left(x+2\right)}\right)\)\(:\left(\frac{x-2}{x-2}-\frac{3}{x-2}\right)\)
\(=\frac{x^2-4x+4+x^2+4x+4-x^2+3x-6}{\left(x+2\right)\left(x-2\right)}:\frac{x-2-3}{x-2}\)
\(=\frac{x^2+3x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\)
\(=\frac{x^2+x+2x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\).
\(=\frac{x\left(x+1\right)+2\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{\left(x+2\right)\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-2}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-5}\)
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\(\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}\)
\(=\frac{\left(x+2\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{x+3}{\left(x-2\right)\left(x+3\right)}\)
\(=\frac{x^2-4-5-x-3}{\left(x+3\right)\left(x-2\right)}\)
\(=\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\)
\(=\frac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}\)
\(=\frac{x-4}{x-2}\)