Question

Упростить. 4,5,6
С решением.

Answer 1

4
$1)2/ sqrt{y} :( sqrt{x} +1/ sqrt{y})=2/ sqrt{y} * sqrt{y} /( sqrt{xy} +1)=2/( sqrt{xy}+1)$
$2)( sqrt{x^3} +1/ sqrt{y^3} )*1/(x-1/y) :( sqrt{x}+1/ sqrt{y} )=$$( sqrt{x^3y^3} +1)/ sqrt{y^3} *y/(xy-1)* sqrt{y} /( sqrt{xy} +1)=$$( sqrt{xy} +1)(xy- sqrt{xy}+1)/(xy-1)( sqrt{xy} +1)=(xy- sqrt{xy} +1)/(xy-$$1)$
$3) sqrt{x}/ sqrt{y} :(x-1/y)= sqrt{x} / sqrt{y} *y/(xy-1)= sqrt{xy} /(xy-1)$
$4)2/( sqrt{xy} +1)+(xy- sqrt{xy} +1)/( sqrt{xy} -1)( sqrt{xy}+1) - sqrt{xy}/( sqrt{xy} -1$$)( sqrt{xy} +1)=(2 sqrt{xy} -2+xy- sqrt{xy} +1- sqrt{xy})/(xy-1)=(xy-1)/($$xy-1)=1$
5
$1)( sqrt{x^3} + sqrt{y^3})/(x- sqrt{xy} +y)=( sqrt{x} + sqrt{y} )(x- sqrt{xy} +y)/(x- sqrt{xy} +$$y)= sqrt{x} + sqrt{y}$
$2)2xy*(1/ sqrt{x} -1/ sqrt{y}):(x-y)= 2xy( sqrt{y} - sqrt{x} )/ sqrt{xy}( sqrt{x}- sqrt{y})( sqrt{x}$$+ sqrt{y})=-2 sqrt{xy}/( sqrt{x} + sqrt{y} )$
$3)( sqrt{x} + sqrt{y} )-2 sqrt{xy}/( sqrt{x} + sqrt{y})=(x+2 sqrt{xy} +y-2 sqrt{xy} )/( sqrt{x} + sqrt{y}$$)=(x+y)/( sqrt{x} + sqrt{y} )$
$4)(x+y)/( sqrt{x} + sqrt{y}):( sqrt{x} - sqrt{y})/(x-y)=(x+y)(x-y)/( sqrt{x}- sqrt{y} )$$( sqrt{x} + sqrt{y} )=(x+y)(x-y)/(x-y)=x+y$
6
$1)(a ^{3/4} +b ^{3/4} )(a ^{3/4} -b ^{3/4} )/( sqrt{a} - sqrt{b})=( sqrt{a^3}- sqrt{b^3} )/( sqrt{a}- sqrt{b} )=$$( sqrt{a} - sqrt{b})(a+ sqrt{ab} +b)/( sqrt{a} - sqrt{b})=a+ sqrt{ab}+b$
$2)a+ sqrt{ab} +b- sqrt{ab} =a+b$
$3)(a+b)*5/(a+b)=5$