Question

RÚT GỌN BT A= \(\dfrac{\sqrt{X}-\sqrt{Y}}{\sqrt{X}+\sqrt{Y}}+\dfrac{\sqrt{X}+\sqrt{Y}}{\sqrt{X}-\sqrt{Y}}-\dfrac{4Y}{X-Y}\)

Answer 1

k chép lại đề:

\(=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+\left(\sqrt{x}+\sqrt{y}\right)^2-4y}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}=\dfrac{x-2\sqrt{xy}+y+x+2\sqrt{xy}+y-4y}{x-y}=\dfrac{2x-2y}{x-y}=\dfrac{2\left(x-y\right)}{\left(x-y\right)}=2\)

Answer 2

\(A=\dfrac{\sqrt{X}-\sqrt{Y}}{\sqrt{X}+\sqrt{Y}}+\dfrac{\sqrt{X}+\sqrt{Y}}{\sqrt{X}-\sqrt{Y}}-\dfrac{4Y}{X-Y}=\dfrac{\left(\sqrt{X}-\sqrt{Y}\right)^2}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}+\dfrac{\left(\sqrt{X}+\sqrt{Y}\right)^2}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}-\dfrac{4Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=\dfrac{X-2\sqrt{XY}+Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}+\dfrac{X+2\sqrt{XY}+Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}-\dfrac{4Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=\dfrac{X-2\sqrt{XY}+Y+X+2\sqrt{XY}+Y-4Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=\dfrac{2X-2Y}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=\dfrac{2\left(X-Y\right)}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=\dfrac{2\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}=2\)

Answer 3

A = \(\dfrac{\left(\sqrt{X}-\sqrt{Y}\right)^2+\left(\sqrt{X}+\sqrt{Y}\right)^2}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}-\dfrac{4X}{X-Y}\)

= \(\dfrac{X-2\sqrt{XY}+Y+X+Y+2\sqrt{XY}}{\left(\sqrt{X}+\sqrt{Y}\right)\left(\sqrt{X}-\sqrt{Y}\right)}-\dfrac{4X}{X-Y}\)

= \(\dfrac{2X+2Y-4X}{X-Y}=\dfrac{-2X+2Y}{X-Y}=\dfrac{-2\left(X-Y\right)}{X-Y}=-2\)