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![](https://rs.olm.vn/images/avt/0.png?1311)
(Vì x > 0 nên |x| = x; y 2 > 0 với mọi y ≠ 0)
(Vì x 2 ≥ 0 với mọi x; và vì y < 0 nên |2y| = – 2y)
(Vì
x
2
y
4
=
(
x
y
2
)
2
>
0
với mọi x ≠ 0, y ≠ 0)
(Vì x < 0 nên |5x| = – 5x; y > 0 nên | y 3 | = y 3 )
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=\dfrac{x\sqrt{y}+y\sqrt{x}}{x+2\sqrt{xy}+y}\)
\(A=\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)^2}\)
\(A=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
b) \(B=\dfrac{x\sqrt{y}-y\sqrt{x}}{x-2\sqrt{xy}+y}\)
\(B=\dfrac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\left(\sqrt{x}-\sqrt{y}\right)^2}\)
\(B=\dfrac{\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\)
c) \(C=\dfrac{3\sqrt{a}-2a-1}{4a-4\sqrt{a}+1}\)
\(C=\dfrac{-\left(2a-3\sqrt{a}+1\right)}{\left(2\sqrt{a}\right)^2-2\sqrt{a}\cdot2\cdot1+1^2}\)
\(C=\dfrac{-\left(\sqrt{a}-1\right)\left(2\sqrt{a}-1\right)}{\left(2\sqrt{a}-1\right)^2}\)
\(C=\dfrac{-\sqrt{a}+1}{2\sqrt{a}-1}\)
d) \(D=\dfrac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\dfrac{4-a}{\sqrt{a}-2}\)
\(D=\dfrac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}+2}+\dfrac{\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)}{\sqrt{a}-2}\)
\(D=\sqrt{a}+2-\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}-2}\)
\(D=\left(\sqrt{a}+2\right)-\left(\sqrt{a}+2\right)\)
\(D=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5xy.\sqrt{\frac{25x^2}{y^6}}=5xy.\sqrt{\frac{5^2x^2}{\left(y^3\right)^2}}=5xy.\sqrt{\frac{\left(5x\right)^2}{\left(y^3\right)^2}}5xy.\sqrt{\left(\frac{5x}{y^3}\right)^2}=5xy.\frac{5x}{y^3}=\frac{5^2x^2}{y^2}=\frac{\left(5x\right)^2}{y^2}=\left(\frac{5x}{y}\right)^2\)
Chúc bạn học tốt
5xy.\(\sqrt{\frac{25x^2}{y^6}}\)
=5xy.\(\frac{\left|5x\right|}{\left|y^3\right|}\){x<0 nên |5x|=-5x
=\(\orbr{\begin{cases}5xy.\frac{-5x}{y^3}\\5xy.\frac{-5x}{-y^3}\end{cases}}\)
=\(\orbr{\begin{cases}\frac{-25x^2}{y^3}\\\frac{25x^2}{y^3}\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a/ \(\frac{y}{x}.\left(\sqrt{\frac{x^2}{y^4}}\right)=\frac{y}{x}.\frac{x}{y^2}=\frac{1}{y}\)
b/ \(2y^2.\sqrt{\frac{x^4}{4y^2}}=2y^2.\sqrt{\frac{\left(x^2\right)^2}{\left(-2y\right)^2}}=2y^2.\frac{x^2}{-2y}=-y.x^2\)
c/ \(5xy.\sqrt{\frac{25x^2}{y^6}}=5xy.\sqrt{\frac{\left(-5x\right)^2}{\left(y^3\right)^2}}=5xy.\frac{-5x}{y^3}=\frac{-25x^2}{y^2}\)
d/\(0,2.x^3y^3.\sqrt{\frac{4^2}{\left(x^2y^4\right)^2}}=\frac{1}{5}.x^3y^3.\frac{4}{x^2y^4}=\frac{4x}{5y}\)
Trần Việt Linh sai phần b,c,d r bn
Sửa lại:
b) 2y\(^2\).\(\sqrt{\frac{x^4}{4y^2}}\) với y<0
Ta có : 2y\(^2\).\(\sqrt{\frac{x^4}{4y^2}}\)=2y\(^2\).\(\frac{x^2}{\left|y\right|}\)
Vì y>0 nên |y| = -y.Ta có : 2y\(^2\).\(\frac{x^2}{2\left|y\right|}\)= -2y\(^2\).\(\frac{x^2}{2y}\) = -2x\(^2\)y
c) 5xy.\(\sqrt{\frac{25x^2}{y^6}}\) với x<0,y>0
Ta có :5xy\(\sqrt{\frac{25x^2}{y^6}}\)=5xy.\(\frac{5\left|x\right|}{y^3}\) ( y>0)
Vì x<0 nên |x| =-x .Ta có : 5xy.\(\frac{5\left|x\right|}{y^3}\)= -5xy.\(\frac{5x}{y^3}\) =\(\frac{-25x^2}{y^2}\)
d) 0,,2x\(^3\)y\(^3\).\(\sqrt{\frac{16}{x^4y^8}}\) với x#o,y#0
Ta có: 0,2x\(^3\)y\(^3\)\(\frac{4}{x^2y^4}\)=\(\frac{0,8x}{y}\) ( vì #0,y#0)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
=
.
=
.
=
vì x > 0.
Do đó
=
.
b)
=
.
=
.
.
Vì y < 0 nên │y│= -y. Do đó
=
.
=
.
c) 5xy.
= 5xy.
= 5xy.
.
Vì x < 0, y > 0 nên
= -x và
=
.
Do đó: 5xy
= 5xy.
= -
.
d) 0,2
=
= 0,2
= ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B0%2C8x%5E%7B2%7D%7D%7B%5Cleft%20%7C%20x%5E%7B3%7D%20%5Cright%20%7Cy%7D)
Nếu x > 0 thì
> 0 nên
. Do đó 0,2
=
.
Nếu x < 0 thì
< 0 nên
. Do đó 0,2
= -
.
a)
=
.
=
.
=
vì x > 0.
Do đó
=
.
b)
=
.
=
.
.
Vì y < 0 nên │y│= -y. Do đó
=
.
=
.
c) 5xy.
= 5xy.
= 5xy.
.
Vì x < 0, y > 0 nên
= -x và
=
.
Do đó: 5xy
= 5xy.
= -
.
d) 0,2
=
= 0,2
= ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B0%2C8x%5E%7B2%7D%7D%7B%5Cleft%20%7C%20x%5E%7B3%7D%20%5Cright%20%7Cy%7D)
Nếu x > 0 thì
> 0 nên
. Do đó 0,2
=
.
Nếu x < 0 thì
< 0 nên
. Do đó 0,2
= -
.