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a, dk \(x\ge0.x\ne1\)
\(\left(\frac{1+\sqrt{x}+1-\sqrt{x}}{2\left(1-x\right)}-\frac{x^2+1}{1-x^2}\right)\left(\frac{x+1}{x}\right)\)=\(\left(\frac{1}{1-x}-\frac{x^2+1}{1-x^2}\right)\left(\frac{x+1}{x}\right)\)
=\(\left(\frac{1+x-x^2-1}{1-x^2}\right)\left(\frac{x+1}{x}\right)=\frac{x\left(1-x\right)\left(x+1\right)}{x\left(1-x\right)\left(1+x\right)}=1\)
phan b,c ban tu lam not nhe dai lam mk ko lam dau mk co vc ban rui
ĐK : x>0, x khác 1
\(A=\left(\frac{1}{\sqrt{x}+1}+\frac{2\left(1-\sqrt{x}\right)}{x\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)}\right):\left(\frac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}-\frac{2}{x-1}\right)\)
\(=\left(\frac{1}{\sqrt{x}+1}-\frac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\right):\left(\frac{1}{\sqrt{x}-1}-\frac{2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)
\(=\frac{\sqrt{x}+1-2}{\left(\sqrt{x}+1\right)^2}:\frac{\sqrt{x}+1-2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)^2}.\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
Trả lời:
\(A=\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right)\div\left(\frac{1}{\sqrt{x}+1}+\frac{2}{x-1}\right)\)
\(A=\left[\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\right]\div\left[\frac{1}{\sqrt{x}+1}+\frac{2}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\right]\)
\(A=\left[\frac{\sqrt{x}.\sqrt{x}}{\sqrt{x}.\left(\sqrt{x}-1\right)}-\frac{1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\right]\div\left[\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}+\frac{2}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\right]\)
\(A=\left[\frac{x-1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\right]\div\left[\frac{\sqrt{x}-1+2}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\right]\)
\(A=\left[\frac{x-1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\right]\div\left[\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\right]\)
\(A=\frac{x-1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\div\frac{1}{\sqrt{x}-1}\)
\(A=\frac{x-1}{\sqrt{x}.\left(\sqrt{x}-1\right)}\times\frac{\sqrt{x}-1}{1}\)
\(A=\frac{x-1}{\sqrt{x}}\)
Học tốt
\(P=\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}+\dfrac{x-1}{\sqrt{x}}\cdot\dfrac{x+2\sqrt{x}+1+x-2\sqrt{x}+1}{x-1}\)
\(=2+\dfrac{2x+2}{\sqrt{x}}=\dfrac{2x+2\sqrt{x}+2}{\sqrt{x}}\)
A=\(\frac{x+1}{\sqrt{x}}-\left(\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)
=\(\frac{x+1}{\sqrt{x}}-\left(\frac{x+\sqrt{x}+1}{\sqrt{x}}-\frac{x-\sqrt{x}+1}{\sqrt{x}}\right)\)
=\(\frac{x+1}{\sqrt{x}}-\frac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}\)
=\(\frac{x+1}{\sqrt{x}}-\frac{2\sqrt{x}}{\sqrt{x}}\)
=\(\frac{x+1-2\sqrt{x}}{\sqrt{x}}\)
A =\(\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}\)