ai giúp mình với ạ

\((\frac{\sqrt{x}+1}{2\sqrt{x}-2}-\frac{\sqrt{x}-1}{2\sqrt{x}+2}-\frac{\sqrt{x}+1}{1-x})\div\frac{x+2\sqrt{x}}{x+\sqrt{x}}\)

\(=(\frac{\sqrt{x}+1}{2(\sqrt{x}-1)}-\frac{\sqrt{x}-1}{2(\sqrt{x}+1)}+\frac{\sqrt{x}+1}{x-1})\div\frac{\sqrt{x}(\sqrt{x}+2)}{\sqrt{x}(\sqrt{x}+1)}\)

\(=(\frac{(\sqrt{x}+1)^2+\left(\sqrt{x}-1\right)^2+2\left(x-1\right)}{2(x-1)}\div\frac{(\sqrt{x}+2)}{(\sqrt{x}+1)}\)

Khai triển ra nhé, mk làm như trên thì lâu lắm nên bn tự lm nhé

\(=\frac{2\left(3\sqrt{x}+1\right)}{2(x-1)}\times\frac{\sqrt{x}+1}{\sqrt{x}+2}\)

\(=\frac{(3\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+2)}\)

come mon

A=\(\frac{x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)

=\(\frac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

=\(\frac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}}{\sqrt{x-2}}\)

Vậy A=\(\frac{\sqrt{x}}{\sqrt{x}-2}\)vs x\(\ge0;x\ne4\)

C=\(\left(\frac{1+x}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\times\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}=\frac{1+x}{\sqrt{x}}\)

Vậy C=\(\frac{1+x}{\sqrt{x}}\)vs x>0

\(\sqrt{x}=y\\ \)

ĐK: \(x\ne0,1,4\Leftrightarrow\left\{\begin{matrix}y>0\\y\ne1\&4\end{matrix}\right.\) ko sửa được y khác 1 &2

\(P=\left(\frac{\left(1-y\right)}{\left(y-2\right)}+\frac{y}{\left(y-1\right)}+\frac{y+2}{\left(y-1\right)\left(y-2\right)}\right):\left(\frac{2}{y-2}-\frac{y-1}{y\left(y-2\right)}\right)\)

\(P=\left(\frac{2y-y^2-1}{\left(y-2\right)\left(y-1\right)}+\frac{y^2-2y}{\left(y-1\right)\left(y-2\right)}+\frac{y+2}{\left(y-1\right)\left(y-2\right)}\right):\left(\frac{2y-y+1}{y\left(y-2\right)}\right)\)

\(P=\left(\frac{y+1}{\left(y-1\right)\left(y-2\right)}\right).\left(\frac{y\left(y-2\right)}{\left(y+1\right)}\right)=\frac{y}{y-1}\)

a) \(P=\frac{\sqrt{x}}{\sqrt{x}-1}\)

b)\(x=6-2\sqrt{5}=5-2\sqrt{5}+1=\left(\sqrt{5}-1\right)^2\)

\(p=\frac{\left(\sqrt{5}-1\right)}{\sqrt{5}-2}=\left(\sqrt{5}-1\right)\left(\sqrt{5}+2\right)=3-\sqrt{5}\)

C)\(\frac{P}{\sqrt{x}}=\frac{1}{\sqrt{x}-1}\ge-1\) tuy nhiên đk: x khác 0=> dấu đẳng thức không xẩy ra (xem lại đề)

Xem lại 1/(căn(x)-1) có cực trị duy nhất khi x=0 tuy nhiên nó cũng không phải GTLN : rất có thể rút gọn P bị sai nếu không đề sai.

????

\(B=\frac{-2a\sqrt{a}+2a^2}{\left(\sqrt{a}-\right)\left(a-1\right)}\)

\(C=-x\sqrt{x}+x+\sqrt{x}-1\)

\(D=x-\sqrt{x}+1\)

có đáp án kĩ hơn không ạ ?