Solve for: номер

Expression: $\frac{ {y}^{2}-\frac{ 2 }{ y } }{ \frac{ 5 }{ y-1 }+y }$

Write all numerators above the common denominator

$\frac{ \frac{ {y}^{3}-2 }{ y } }{ \frac{ 5 }{ y-1 }+y }$

Write all numerators above the common denominator

$\frac{ \frac{ {y}^{3}-2 }{ y } }{ \frac{ 5+y \times \left( y-1 \right) }{ y-1 } }$

Distribute $y$ through the parentheses

$\frac{ \frac{ {y}^{3}-2 }{ y } }{ \frac{ 5+{y}^{2}-y }{ y-1 } }$

Simplify the complex fraction

$\frac{ \left( {y}^{3}-2 \right) \times \left( y-1 \right) }{ y \times \left( 5+{y}^{2}-y \right) }$

Simplify the expression

$\frac{ {y}^{4}-{y}^{3}-2y+2 }{ y \times \left( 5+{y}^{2}-y \right) }$

Distribute $y$ through the parentheses

$\frac{ {y}^{4}-{y}^{3}-2y+2 }{ 5y+{y}^{3}-{y}^{2} }$

Use the commutative property to reorder the terms

$\frac{ {y}^{4}-{y}^{3}-2y+2 }{ {y}^{3}-{y}^{2}+5y }$