Khử mẫu biểu thức sau -2xy - 9 x 3 y 2 với x < 0; y > 0 ta được:
A. - 6 x
B. - 6 - x
C. 6 x
D. - 6 x
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Khử mẫu biểu thức sau -2xy - 9 x 3 y 2 với x < 0; y > 0 ta được:
A. - 6 x
B. - 6 - x
C. 6 x
D. - 6 x
a: \(=6\cdot\sqrt{\dfrac{2xy}{4y^2}}\)
\(=6\cdot\dfrac{\sqrt{2xy}}{-2y}=-\dfrac{3\sqrt{2xy}}{y}\)
b: \(=\dfrac{4xy^2}{3}\cdot\dfrac{3}{\sqrt{xy}}=4\sqrt{x}\cdot y\sqrt{y}\)
a: \(\sqrt{\dfrac{3}{20}}=\sqrt{\dfrac{15}{100}}=\dfrac{\sqrt{15}}{10}\)
b: \(\sqrt{\dfrac{5}{18}}=\sqrt{\dfrac{10}{36}}=\dfrac{\sqrt{10}}{6}\)
c: \(ab\sqrt{\dfrac{a}{b}}=ab\cdot\dfrac{\sqrt{a}}{\sqrt{b}}=a\sqrt{ab}\)
d: \(\dfrac{x}{y}\sqrt{\dfrac{y}{x}}=\dfrac{x}{y}\cdot\dfrac{\sqrt{y}}{\sqrt{x}}=\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{xy}}{y}\)
a) \(\sqrt{\frac{3}{2}}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{3}.\sqrt{2}}{2}=\frac{\sqrt{6}}{2}\)
b) \(\sqrt{\frac{3a}{5b}}=\frac{\sqrt{3a}}{\sqrt{5b}}=\frac{\sqrt{3a}.\sqrt{5b}}{5b}=\frac{\sqrt{15ab}}{5b}\left(a;b>0\right)\)
c) \(\sqrt{\frac{5}{12}}=\frac{\sqrt{5}}{\sqrt{12}}=\frac{\sqrt{5}.\sqrt{12}}{12}=\frac{\sqrt{60}}{12}=\frac{2\sqrt{15}}{12}=\frac{\sqrt{15}}{6}\)
d) \(\sqrt{\frac{5x}{18y}}=\frac{\sqrt{5x}}{\sqrt{18y}}=\frac{\sqrt{5x}}{\sqrt{3^2.2y}}=\frac{\sqrt{5x}}{3\sqrt{2y}}\)
\(=\frac{\sqrt{5x}.\sqrt{3y}}{3.2y}=\frac{\sqrt{15xy}}{6xy}\)
a) \(\dfrac{3-\sqrt{x}}{x-9}=\dfrac{-\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=-\dfrac{1}{\sqrt{x+3}}\)(\(x\ge0,x\ne9\))
b) \(\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}{\sqrt{x}-3}=\sqrt{x}-2\left(x\ge0,x\ne9\right)\)
a) \(\dfrac{3-\sqrt{x}}{x-9}=\dfrac{3-\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=-\dfrac{1}{\sqrt{x}+3}\)
b) \(\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\sqrt{x}-3}=\sqrt{x}-2\)
c) \(6-2x-\sqrt{9-6x+x^2}=6-2x-\sqrt{\left(3-x\right)^2}=6-2x-\left|3-x\right|\)
mà \(x< 3\Rightarrow3-x>0\Rightarrow6-2x-\left|3-x\right|=6-2x-3+x=3-x\)
\(\dfrac{1}{y-x}\cdot\sqrt{x^6\left(x-y\right)^2}\)
\(\dfrac{1}{y-x}\cdot x^3\cdot\left(x-y\right)\)
\(=-x^3\)