Question

ayuda es para mañana
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Answer 1

Respuesta:

Explicación paso a paso:

$A)\ \ \dfrac{x+y}{\dfrac{1}{x}+\dfrac{1}{y}}=xy\\\\\\\dfrac{x+y}{\dfrac{y+x}{xy}}=xy\\\\\\\dfrac{x+y}{\dfrac{x+y}{xy}}=xy\\\\\\\dfrac{x+y}{1}\times\dfrac{xy}{x+y}=xy\\\\\\ \boxed{xy=xy}$

 

$B)\ \ \ \dfrac{2+\dfrac{1}{x}}{2x^2+x}=\dfrac{1}{x^2}\\\\\\\dfrac{\dfrac{2x+1}{x}}{x(2x+1)}=\dfrac{1}{x^2}\\\\\\\dfrac{(2x+1)}{x}\times\dfrac{1}{x(2x+1)}=\dfrac{1}{x^2}\\\\\\\dfrac{1}{x}\times\dfrac{1}{x}\\\\\\\ \boxed{\dfrac{1}{x^2}=\dfrac{1}{x^2}}$

 

$C)\ \ \ \dfrac{(y+\frac{2y}{y-2})}{(1+\frac{4}{y^2-4})}=y+2\\\\\\\dfrac{\dfrac{y(y-2)+2y}{y-2}}{\dfrac{y^2-4+4}{y^2-4}}=y+2\\\\\\\dfrac{\dfrac{y^2-2y+2y}{y-2}}{\dfrac{y^2}{(y-2)(y+2)}}=y+2\\\\\\\dfrac{\dfrac{y^2}{y-2}}{\dfrac{y^2}{(y-2)(y+2)}}=y+2$

$\dfrac{y^2}{(y-2)}\times\dfrac{(y-2)(y+2)}{y^2}=y+2\\\\\\\dfrac{1}{1}\times\dfrac{y+2}{1}=y+2\\\\\\\boxed{y+2=y+2}$