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\(A=4\sqrt{x}-\frac{x+6\sqrt{x}+9}{x-9}\)
\(=4\sqrt{x}-\frac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=4\sqrt{x}-\frac{\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)}\)
\(=\frac{4\sqrt{x}\left(\sqrt{x}-3\right)}{\sqrt{x}-3}-\frac{\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)}\)
\(=\frac{4x-12\sqrt{x}-\sqrt{x}-3}{\sqrt{x}-3}\)
\(=\frac{4x-13\sqrt{x}-3}{\sqrt{x}-3}\)
C.Tham khảo ở dây:Câu hỏi của Đặng Phương Thảo - Toán lớp 9 - Học toán với OnlineMath
\(B=\frac{5\sqrt{x}-\left(x-10\sqrt{x}+25\right)\left(\sqrt{x}+5\right)}{x-25}\)
\(=\frac{5\sqrt{x}-\left(\sqrt{x}-5\right)^2\left(\sqrt{x}+5\right)}{x-25}\)
\(=\frac{5\sqrt{x}-\left(\sqrt{x}-5\right)\left(x-25\right)}{x-25}\)
\(=\frac{5\sqrt{x}-\left(x\sqrt{x}-25\sqrt{x}-5x+125\right)}{x-25}\)
\(=\frac{5\sqrt{x}-x\sqrt{x}+25\sqrt{x}+5x-125}{x-25}\)
\(=\frac{-x\sqrt{x}+30\sqrt{x}+5x-125}{x-25}\)
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ĐKXĐ:...
\(\left(\frac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}-1\right):\left(\frac{25-x}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}-\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}+\frac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}\right)\)
\(=\left(\frac{\sqrt{x}-\sqrt{x}-5}{\sqrt{x}+5}\right):\left(\frac{25-x-x+9+x-25}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}\right)=\frac{-5}{\left(\sqrt{x}+5\right)}.\frac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}{\left(9-x\right)}\)
\(=\frac{5\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\frac{5}{\sqrt{x}+3}\)
\(A=2-x\sqrt{\frac{x\left(x-2\right)}{\left(x-2\right)^2}+\frac{1}{\left(x-2\right)^2}}=2-x\sqrt{\frac{\left(x-1\right)^2}{\left(x-2\right)^2}}\)
\(=2-x\cdot\frac{x-1}{x-2}=\frac{2x-4}{x-2}-\frac{x^2-x}{x-2}=\frac{-x^2+3x-4}{x-2}\)
\(B=\frac{2\sqrt{5}x}{x-2}\cdot\left|x-2\right|+\frac{3\sqrt{5}x^2}{x}=\frac{2\sqrt{5}x}{x-2}\cdot\left|x-2\right|+3\sqrt{5}x\)
Với 0 < x < 2 \(B=-2\sqrt{5}x+3\sqrt{5}x=\sqrt{5}x\)
Với x > 2 \(B=2\sqrt{5}x+3\sqrt{5}x=5\sqrt{5}x\)
\(C=\frac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\sqrt{x}\left(\sqrt{x}+5\right)}+\sqrt{\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-5\right)^2}}=\frac{\sqrt{x}-5}{\sqrt{x}}+\left|\frac{\sqrt{x}-1}{\sqrt{x}-5}\right|\)
Với 0 < x < 1 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}+\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}+\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{2x-11\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)
Với 1 < x < 5 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}-\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}-\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{-9\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)
Với x > 5 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}+\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}+\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{2x-11\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)
ĐKXĐ: ...
\(A=\left(\frac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}-1\right):\left(\frac{25-x+\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}-\frac{\sqrt{x}+3}{\sqrt{x}+5}\right)\)
\(=\left(\frac{\sqrt{x}}{\sqrt{x}+5}-\frac{\sqrt{x}+5}{\sqrt{x}+5}\right):\left(\frac{25-x+x-25}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}-\frac{\sqrt{x}+3}{\sqrt{x}+5}\right)\)
\(=\frac{-5}{\left(\sqrt{x}+5\right)}.\frac{\left(\sqrt{x}+5\right)}{-\left(\sqrt{x}+3\right)}=\frac{5}{\sqrt{x}+3}\)
b/ \(B=\frac{x+16}{\sqrt{x}+3}=\sqrt{x}-3+\frac{25}{\sqrt{x}+3}=\sqrt{x}+3+\frac{25}{\sqrt{x}+3}-6\)
\(\Rightarrow B\ge2\sqrt{\frac{\left(\sqrt{x}+3\right).25}{\sqrt{x}+3}}-6=4\)
\(B_{min}=4\) khi \(\left(\sqrt{x}+3\right)^2=25\Rightarrow x=4\)
a. P=\(\frac{x-5\sqrt{x}-x+25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}:\frac{25-x-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)+\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}{\cdot\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{-5\left(\sqrt{x}-5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}:\frac{-x+9}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{-5}{\sqrt{x}+5}.\frac{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}{-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\frac{5}{\sqrt{x}+3}\)
b. P=\(\frac{5}{\sqrt{x}+3}\)
P nguyên \(\Leftrightarrow\sqrt{x}+3\inƯ\left(5\right)\Rightarrow\sqrt{x}+3\in\left\{-5;-1;1;5\right\}\)
\(\Rightarrow\sqrt{x}\in\left\{2\right\}\)\(\Rightarrow x=4\)
Vậy x=4 thì P nguyên
ĐKXĐ :\(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-3\ne0\\\sqrt{x}+5\ne0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne3\\\sqrt{x}\ne-5\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x\ge0\\x\ne9\end{matrix}\right.\)
- Ta có : \(\left(\frac{x-5\sqrt{x}}{25}-1\right):\left(\frac{25-x}{x+2\sqrt{x}-15}-\frac{\sqrt{x}+3}{\sqrt{x}+5}+\frac{\sqrt{x}-5}{\sqrt{x}-3}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{25-x}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+3}{\sqrt{x}+5}+\frac{\sqrt{x}-5}{\sqrt{x}-3}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{25-x}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}+\frac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{25-x}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}-\frac{x-9}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}+\frac{x-25}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{25-x-x+9+x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{-x+9}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right):\left(\frac{-\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{x-5\sqrt{x}-25}{25}\right)\left(\frac{\sqrt{x}+5}{-\sqrt{x}-3}\right)\)
\(=\frac{\left(x-5\sqrt{x}-25\right)\left(\sqrt{x}+5\right)}{-25\left(\sqrt{x}+3\right)}=\frac{x\sqrt{x}+5x-5x-25\sqrt{x}-25\sqrt{x}-125}{-25\left(\sqrt{x}+3\right)}\)
\(=\frac{x\sqrt{x}-125-50\sqrt{x}}{-25\left(\sqrt{x}+3\right)}\)
\(\left(\sqrt{4,5}-\frac{1}{2}.\sqrt{72}+5\sqrt{\frac{1}{2}}\right).\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
=\(\left(\frac{3\sqrt{2}}{2}-3\sqrt{2}+\frac{5\sqrt{2}}{2}\right).\left(35\sqrt{6}-5\sqrt{6}-28\sqrt{6}\right)\)
=\(\left(\frac{3\sqrt{2}-6\sqrt{2}+5\sqrt{2}}{2}\right).2\sqrt{6}\)
=\(2\sqrt{2}.\sqrt{6}=4\sqrt{3}\)
ĐKXĐ : \(x\ge0;x\ne25\)
Ta có : \(5\sqrt{x}-\frac{\left(x-10\sqrt{x}+25\right)\left(\sqrt{x}+5\right)}{x-25}\)
\(=5\sqrt{x}-\frac{\left(\sqrt{x}-5\right)^2\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)
\(=5\sqrt{x}-\left(\sqrt{x}-5\right)\)
\(=4\sqrt{x}+5\)