Question

упростите подробно пожалуйста)
$( frac{x sqrt{y} + y sqrt{x} }{ y^{2} - x^{2} } )( frac{ sqrt{x}}{x- sqrt{xy} } + frac{ sqrt{y} }{y- sqrt{xy} } )=$

Answer 1

$(frac{xsqrt{y}+ysqrt{x}}{y^{2}-x^{2}})(frac{sqrt{x}}{x-sqrt{xy}} + frac{sqrt{y}}{y-sqrt{xy}})=\ =(frac{xsqrt{y}+ysqrt{x}}{y^{2}-x^{2}})(frac{sqrt{x}}{sqrt{x}(sqrt{x}-sqrt{y})} + frac{sqrt{y}}{sqrt{y}(sqrt{y}-sqrt{x})})=\ =(frac{xsqrt{y}+ysqrt{x}}{y^{2}-x^{2}})(frac{1}{sqrt{x}-sqrt{y}} + frac{1}{sqrt{y}-sqrt{x}})=\ =(frac{xsqrt{y}+ysqrt{x}}{y^{2}-x^{2}})(frac{1}{sqrt{x}-sqrt{y}} - frac{1}{sqrt{x}-sqrt{y}})=\ =(frac{xsqrt{y}+ysqrt{x}}{y^{2}-x^{2}})*0=0$