HOC24
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\(\dfrac{4x-3}{x-1}< 5\)
\(\Leftrightarrow4x-3< 5\left(x-1\right)\)
\(\Leftrightarrow4x-3< 5x-5\)
\(\Leftrightarrow4x-3-5x+5< 0\)
\(\Leftrightarrow-x+2< 0\)
\(\Leftrightarrow-x< -2\)
\(\Leftrightarrow x>2\)
Vậy x > 2
ĐKXĐ: \(a\ge0,a\ne1\)
\(A=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)
\(A=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{\left(\sqrt{a}+1\right)\left(\sqrt{a-1}\right)}\right)\)
\(A=\dfrac{a-1}{\sqrt{a}\left(a-1\right)}:\left(\dfrac{\sqrt{a}-1+2}{\left(\sqrt{a}+1\right)\left(\sqrt{a-1}\right)}\right)\)
\(A=\dfrac{1}{\sqrt{a}}.\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}+1}\)
\(A=\dfrac{1}{\sqrt{a}}.\left(\sqrt{a}-1\right)=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)