Question

Answer 1

\(\dfrac{3\sqrt{x-1}-2}{\sqrt{x-1}-1}-4=0\left(x\ge1;x\ne2\right)\\ \Leftrightarrow\dfrac{3\sqrt{x-1}-2-4\left(\sqrt{x-1}-1\right)}{\sqrt{x-1}-1}=0\\ \Leftrightarrow3\sqrt{x-1}-2-4\sqrt{x-1}+4=0\\ \Leftrightarrow\sqrt{x-1}=2\\ \Leftrightarrow x-1=4\Leftrightarrow x=5\left(TM\right)\)

Answer 2

Ta có: \(\dfrac{3\sqrt{x-1}-2}{\sqrt{x-1}-1}-4=0\)

\(\Leftrightarrow4\sqrt{x-1}-4=3\sqrt{x-1}-2\)

\(\Leftrightarrow\sqrt{x-1}=2\)

\(\Leftrightarrow x-1=4\)

hay x=5