If (x^{3/2} - x y^{1/2} + x^{1/2} y - y^{3/2} | vedclass

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(A) Given expression: $x^{3/2} - x y^{1/2} + x^{1/2} y - y^{3/2}$Factorize by grouping terms:$= x(x^{1/2} - y^{1/2}) + y(x^{1/2} - y^{1/2})$Take $(x^{

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$x + y$

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(A) Given expression: $x^{3/2} - x y^{1/2} + x^{1/2} y - y^{3/2}$Factorize by grouping terms:$= x(x^{1/2} - y^{1/2}) + y(x^{1/2} - y^{1/2})$Take $(x^{1/2} - y^{1/2})$ as a common factor:$= (x + y)(x^{1/2} - y^{1/2})$Now,divide the expression by $(x^{1/2} - y^{1/2})$:$\frac{(x + y)(x^{1/2} - y^{1/2})}{x^{1/2} - y^{1/2}} = x + y$Therefore,the quotient is $x + y$.

If $(x^{3/2} - x y^{1/2} + x^{1/2} y - y^{3/2})$ is divided by $(x^{1/2} - y^{1/2})$,then the quotient is

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