Question

(x^2 - x^(1/2))/(1-x^(1/2))

Answer 1

x² - x^(1/2) = x²
1 - x^(1/2)

Answer 2

`\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`