Question

\(\dfrac{y+12-4\sqrt{3y}}{y-12}\)

Answer 1

\(\dfrac{y+12-4\sqrt{3y}}{y-12}\) (ĐK: \(y\ge0,y\ne12\)) 

\(=\dfrac{y-4\sqrt{3y}+12}{y-12}\)

\(=\dfrac{\left(\sqrt{y}\right)^2-2\cdot2\sqrt{3}\cdot\sqrt{y}+\left(2\sqrt{3}\right)^2}{y-12}\)

\(=\dfrac{\left(\sqrt{y}-2\sqrt{3}\right)^2}{\left(\sqrt{y}\right)^2-\left(2\sqrt{3}\right)^2}\)

\(=\dfrac{\left(\sqrt{y}-2\sqrt{3}\right)^2}{\left(\sqrt{y}-2\sqrt{3}\right)\left(\sqrt{y}+2\sqrt{3}\right)}\)

\(=\dfrac{\sqrt{y}-2\sqrt{3}}{\sqrt{y}+2\sqrt{3}}\)