Question

Rút gọn

tìm x để B>3

\(\dfrac{1}{\sqrt x-1}-\dfrac{2\sqrt x}{x\sqrt x+ \sqrt x -x -1}\)

Answer 1

\(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\)

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

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

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

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

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