\(\frac { \left( { x }^{ 2 }-{ x }^{ \frac { 1 }{ 2 } } \right) }{ \left( 1-{ x }^{ \frac { 1 }{ 2 } } \right) }\)
\(\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot 1\)
\(\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot \frac { \left( 1+\sqrt { x } \right) }{ \left( 1+\sqrt { x } \right) }\)
\(\\ \\ =\frac { { x }^{ 2 }+{ x }^{ 2 }\sqrt { x } -\sqrt { x } -x }{ 1+\sqrt { x } -\sqrt { x } -x }\)
\(\\ \\ =\frac { -\sqrt { x } \left( 1-{ x }^{ 2 } \right) -x\left( 1-x \right) }{ \left( 1-x \right) }\)
\(\\ \\ =\frac { -\sqrt { x } \left( 1+x \right) \left( 1-x \right) -x\left( 1-x \right) }{ \left( 1-x \right) }\)
\(\\ \\ =\frac { \left( 1-x \right) \left\{ -\sqrt { x } \left( 1+x \right) -x \right\} }{ \left( 1-x \right) }\)
\(\\ \\ =-\sqrt { x } \left( 1+x \right) -x\\ \\ =-{ x }^{ \frac { 1 }{ 2 } }\left( 1+{ x }^{ \frac { 2 }{ 2 } } \right) -x\)
\(\\ \\ =-{ x }^{ \frac { 1 }{ 2 } }-{ x }^{ \frac { 3 }{ 2 } }-x\\ \\ =-\sqrt { x } -\sqrt { { x }^{ 3 } } -x\)
