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a: \(=\dfrac{\sqrt{m}\left(m+4n-4\sqrt{mn}\right)}{\sqrt{mn}\left(\sqrt{m}-2\sqrt{n}\right)}\)
\(=\dfrac{1}{\sqrt{n}}\cdot\left(\sqrt{m}-2\sqrt{n}\right)\)
b: \(=\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+\sqrt{x}+1}{\sqrt{x}+1}\)
c: \(=\sqrt{5^2\cdot2\cdot x^2y^4\cdot xy}-\dfrac{2y^2}{x^2}\cdot4\sqrt{2}\cdot x^3\sqrt{xy}+\dfrac{3}{2}xy\cdot\sqrt{2}\cdot y\cdot\sqrt{xy}\)
\(=5xy^2\sqrt{2xy}-8\sqrt{2xy}xy^2+\dfrac{3}{2}xy^2\cdot\sqrt{2xy}\)
\(=-\dfrac{3}{2}\sqrt{2xy}\)
d: \(=\left(x+2\right)\cdot\dfrac{\sqrt{2x-3}}{\sqrt{x+2}}=\sqrt{\left(2x-3\right)\left(x+2\right)}\)
a)\(\frac{\sqrt{63y^3}}{\sqrt{7}y}=\frac{\sqrt{7\cdot3^2\cdot y^2\cdot y}}{\sqrt{7}y}=\frac{\sqrt{7}\cdot\sqrt{3^2}\cdot\sqrt{y^2}\cdot\sqrt{y}}{\sqrt{7}y}=\frac{\sqrt{7}\cdot3\cdot y\cdot\sqrt{y}}{\sqrt{7}y}=3\sqrt{y}\)
b)\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}=\frac{\sqrt{4^2\cdot3\cdot x^2\cdot x}}{\sqrt{3\cdot x^2\cdot x^3}}=\frac{\sqrt{4^2}\cdot\sqrt{3}\cdot\sqrt{x^3}}{\sqrt{3}\cdot\sqrt{x^2}\cdot\sqrt{x^3}}=\frac{4}{x}\)
c)\(\frac{\sqrt{45mn^2}}{\sqrt{20m}}=\frac{\sqrt{5\cdot3^2\cdot m\cdot n^2}}{\sqrt{5\cdot2^2\cdot m}}=\frac{\sqrt{5}\cdot\sqrt{3^2}\cdot\sqrt{m}\cdot\sqrt{n^2}}{\sqrt{5}\cdot\sqrt{2^2}\cdot\sqrt{m}}=\frac{3\left|n\right|}{2}\)
d)\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\frac{\sqrt{4^2\cdot a^2\cdot a^2\cdot b^2\cdot b^2\cdot b^2}}{\sqrt{4^2\cdot8\cdot a^2\cdot a^2\cdot a^2\cdot b^2\cdot b^2\cdot b^2}}=\frac{\sqrt{4^2}\cdot\sqrt{a^2}\cdot\sqrt{a^2}\cdot\sqrt{b^2}\cdot\sqrt{b^2}\cdot\sqrt{b^2}}{\sqrt{4^2}\cdot\sqrt{8}\cdot\sqrt{a^2}\cdot\sqrt{a^2}\cdot\sqrt{a^2}\cdot\sqrt{b^2}\cdot\sqrt{b^2}\cdot\sqrt{b^2}}=\frac{4\cdot a^2\cdot b^3}{4\cdot\sqrt{8}\cdot\left|a\right|^3\cdot b^3}=\frac{a^2}{\sqrt{8}\left|a\right|^3}\)
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Kết quả rất lẻ : \(\frac{-16y^2\sqrt{x^7y}+3x^3y\sqrt{xy^3}+500x^2\sqrt{y^5}}{\sqrt{2}x^2}\)