Rút gọn biểu thức \(A=\left(1-2\sqrt{\dfrac{b}{a}}+\dfrac{b}{a}\right):\left(a^{\dfrac{1}{2}}-b^{\dfrac{1}{2}}\right)\) ta được
\(A=\dfrac{1}{a}\).\(A=\dfrac{2}{a}\).\(A=\dfrac{\sqrt{a}-\sqrt{b}}{a}\).\(A=\dfrac{\sqrt{a}+\sqrt{b}}{a}\).Hướng dẫn giải:\(A=\left(1-2\sqrt{\dfrac{b}{a}}+\dfrac{b}{a}\right):\left(a^{\dfrac{1}{2}}-b^{\dfrac{1}{2}}\right)\)
\(=\left[1-2\sqrt{\dfrac{b}{a}}+\left(\sqrt{\dfrac{b}{a}}\right)^2\right]:\left(a^{\dfrac{1}{2}}-b^{\dfrac{1}{2}}\right)\)
\(=\left[1-\sqrt{\dfrac{b}{a}}\right]^2:\left(a^{\dfrac{1}{2}}-b^{\dfrac{1}{2}}\right)\)
\(=\left[1-\sqrt{\dfrac{b}{a}}\right]^2:\left(\sqrt{a}-\sqrt{b}\right)\) (ĐK \(a\ge0;b\ge0;a\ne b\))
\(=\left[\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}}\right]^2.\dfrac{1}{\sqrt{a}-\sqrt{b}}\)
\(=\dfrac{\sqrt{a}-\sqrt{b}}{a}\)
