[tex] \frac{ {x}^{ - 2}y + {x}^{2} {y}^{ - 1} }{ {x}^{ - 3} - {y}^{ - 2} } \\ = \frac{ \frac{1}{ {x}^{2} }y + \frac{1}{y} {x}^{2} }{ \frac{1}{ {x}^{3}} - \frac{1}{ {y}^{2} } } \\ = \frac{ \frac{ {y}^{2 } + {x}^{4} }{ {x}^{2}y } }{ \frac{ {y}^{2} - {x}^{3} }{ {x}^{3} {y}^{2} } } \\ = \frac{ {y}^{2} + {x}^{4} }{ {x}^{2}y } \times \frac{ {x}^{3} {y}^{2} }{ {y}^{2} - {x}^{3} } \\ = \frac{xy( {y}^{2} + {x}^{4} )}{ {y}^{2} - {x}^{3} } \\ = \frac{x {y}^{3} + {x}^{5}y }{ {y}^{2} - {x}^{3} } [/tex]
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
[tex] \frac{ {x}^{ - 2}y + {x}^{2} {y}^{ - 1} }{ {x}^{ - 3} - {y}^{ - 2} } \\ = \frac{ \frac{1}{ {x}^{2} }y + \frac{1}{y} {x}^{2} }{ \frac{1}{ {x}^{3}} - \frac{1}{ {y}^{2} } } \\ = \frac{ \frac{ {y}^{2 } + {x}^{4} }{ {x}^{2}y } }{ \frac{ {y}^{2} - {x}^{3} }{ {x}^{3} {y}^{2} } } \\ = \frac{ {y}^{2} + {x}^{4} }{ {x}^{2}y } \times \frac{ {x}^{3} {y}^{2} }{ {y}^{2} - {x}^{3} } \\ = \frac{xy( {y}^{2} + {x}^{4} )}{ {y}^{2} - {x}^{3} } \\ = \frac{x {y}^{3} + {x}^{5}y }{ {y}^{2} - {x}^{3} } [/tex]