\(\frac{3}{\sqrt{7}-1}+\frac{3}{\sqrt{7}+1}=\frac{3\left[\sqrt{7}+1+\sqrt{7}-1\right]}{\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)}=\frac{6\sqrt{7}}{6}=\sqrt{7}\)

\(\frac{3}{\sqrt{X}-1}-\frac{2}{\sqrt{X}+1}+\frac{X-7}{X-1}=\frac{3\left(\sqrt{X}+1\right)-2\left(\sqrt{X}-1\right)+X-7}{\left(\sqrt{X}+1\right)\left(\sqrt{X}-1\right)}=\frac{X+\sqrt{X}-2}{\left(\sqrt{X}+1\right)\left(\sqrt{X}-1\right)}=\frac{\sqrt{X}+2}{\sqrt{X}+1}\)

TÍNH GIÁ TRỊ BIỂU THỨC:

\(\frac{3}{\sqrt{7}-1}\) + \(\frac{3}{\sqrt{7}+1}\)= \(\frac{3\left(\sqrt{7}+1\right)+3\left(\sqrt{7}-1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}\)= \(\frac{3\sqrt{7}+3+3\sqrt{7}-3}{6}\)=\(\frac{6\sqrt{7}}{6}\)=\(\sqrt{7}\)

RÚT GỌN BIỂU THỨC:

\(\frac{3}{\sqrt{X}-1}\)-\(\frac{2}{\sqrt{X}+1}\)+\(\frac{X-7}{X-1}\)

= \(\frac{3\left(\sqrt{X}+1\right)}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)-\(\frac{2\left(\sqrt{X}-1\right)}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)+\(\frac{X-7}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

= \(\frac{3\sqrt{X}+3-2\sqrt{X}+2+X-7}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

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

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

= \(\frac{\sqrt{X}-2}{\sqrt{X}-1}\)

CHÚC EM HỌC TỐT!

Với \(x\ge0;x\ne4\)

\(A=\frac{\sqrt{x}-1}{\sqrt{x}-2}>\frac{5}{4}\Leftrightarrow\frac{\sqrt{x}-1}{\sqrt{x}-2}-\frac{5}{4}>0\)

\(\Leftrightarrow\frac{4\sqrt{x}-4-5\sqrt{x}+10}{4\left(\sqrt{x}-2\right)}>0\Leftrightarrow\frac{6-\sqrt{x}}{4\left(\sqrt{x}-2\right)}>0\)

\(\Leftrightarrow\frac{\sqrt{x}-6}{4\left(\sqrt{x}-2\right)}< 0\)TH1 : \(\hept{\begin{cases}\sqrt{x}-6< 0\\\sqrt{x}-2>0\end{cases}}\Leftrightarrow\hept{\begin{cases}x< 36\\x>4\end{cases}}\Leftrightarrow4< x< 36\)

TH2 : \(\hept{\begin{cases}\sqrt{x}-6>0\\\sqrt{x}-2< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x>36\\x< 4\end{cases}}}\)( vô lí )

Vậy 4 < x < 36 thì A > 5/4 

giúp gì?

giúp j thế

tâm là giao của 2 đường chéo AC và BD