rut gon bieu thuc: \(\frac{\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2}\left(2x+\sqrt{x^2+1}\right)}{\sqrt{\left(x+1\right)^3}-\sqrt{\left(x-1\right)^2}}\)
\(B=\left(\frac{\left(x-2\right)}{x+2\sqrt{x}}+\frac{1}{\sqrt{x}+2}\right).\frac{\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\) rut gon
=\(\frac{x-2+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}.\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}.\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}+1}{\sqrt{x}}\)
Rut gon bieu thuc
B=\(\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\)\(\left(\frac{\sqrt{x}+1}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-1}\right)\)
\(B=\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-1}\right)\)
\(=\frac{\sqrt{x}-\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)\(:\left(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}:\)\(\frac{x-1-x+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}{2}\)
\(=\frac{\sqrt{x}+3}{2\sqrt{x}}\)
CHO: \(P=\left(\frac{\sqrt{x-1}}{3+\sqrt{x-1}}+\frac{x+8}{10-x}\right);\left(\frac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\frac{1}{\sqrt{x-1}}\right)\)
rut gon P
a)\(\left(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+x\sqrt{x}}\right):\frac{2\left(x-2\sqrt{x}+1\right)}{x-1}\)
Rut gon
Tim x de B nguyen
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
Lời giải:
a)
\(=\frac{(\sqrt{x}+1)\sqrt{x}(\sqrt{x}-\sqrt{y}))\sqrt{x}+\sqrt{y})}{(x-y)x(\sqrt{x}+1)}=\frac{(\sqrt{x}+1)\sqrt{x}(x-y)}{(x-y)x\sqrt{x}+1)}=\frac{1}{\sqrt{x}}\)
b)
\(=\frac{(2-\sqrt{x}-\sqrt{x}-3)(2-\sqrt{x}+\sqrt{x}+3)}{1+2\sqrt{x}}=\frac{(-1-2\sqrt{x}).5}{2\sqrt{x}+1}=\frac{-5(2\sqrt{x}+1)}{2\sqrt{x}+1}=-5\)
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
\(a,\frac{\left(\sqrt{x}+1\right)\cdot\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right)\sqrt{x}\left(x+1\right)}\)\(=\frac{\left(\sqrt{x}+1\right)\sqrt{x}\left(x-y\right)}{\left(x-y\right)\sqrt{x} \left(x+1\right)}\)\(=\frac{\sqrt{x}+1}{x+1}\)
\(b,\frac{\left(2-\sqrt{x}\right)^2-\sqrt{x}-3}{1+2\sqrt{x}}=\frac{4+x-4\sqrt{x}-\sqrt{x}-3}{1+2\sqrt{x}}=\frac{1+x-5\sqrt{x}}{1+2\sqrt{x}}\)
\(P=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
a)Rut gon P?
b)Tinh gia tri cua P voi \(x=3-2\sqrt{2}\)?
rut gon roi tim x de p=-2 \(p=\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}}{\sqrt{x}-1}\right):\frac{2}{\sqrt{x}+1}\)
ĐKXĐ: \(x\ge0;x\ne1\)
\(P=\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}}{\sqrt{x}-1}\right):\frac{2}{\sqrt{x}+1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-1\right)-\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\frac{2}{\sqrt{x}+1}\)
\(=\frac{x-\sqrt{x}+x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\frac{2}{\sqrt{x}+1}\)
\(=\frac{-2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\frac{\sqrt{x}+1}{2}\)
\(=\frac{-\sqrt{x}}{\sqrt{x}-1}\)
Để p = -2 \(\Rightarrow\frac{-\sqrt{x}}{\sqrt{x}-1}=-2\)
\(\frac{-\sqrt{x}}{\sqrt{x}-1}=-2\)
\(\Rightarrow-\sqrt{x}=-2\left(\sqrt{x}-1\right)\)
\(\Rightarrow-\sqrt{x}=-2\sqrt{x}+2\)
\(\Rightarrow-\sqrt{x}+2\sqrt{x}=2\)
\(\Rightarrow\sqrt{x}=2\)
\(\Rightarrow x=4\)
