Question

Answer 1

`a)`\(\dfrac{\sqrt{a}-2a}{2\sqrt{a}-1}=-\dfrac{\sqrt{a}\left(2\sqrt{a}-1\right)}{2\sqrt{a}-1}=-\sqrt{a}\)

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

`c)`\(\dfrac{\sqrt{x}-3}{x-9}=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{1}{\sqrt{x}+3}\)

`d)`\(\dfrac{x+\sqrt{x}\sqrt{y}}{x-y}=\dfrac{\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)