Question

Rút gọn

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

Answer 1

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

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

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

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

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

Answer 2