Rewrite \({y}^{4}-1\) in the form \({a}^{2}-{b}^{2}\), where \(a={y}^{2}\) and \(b=1\).
\[\frac{y}{{y}^{2}-\frac{{({y}^{2})}^{2}-{1}^{2}}{y+\frac{1}{y+1}}}\times 23\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{y}{{y}^{2}-\frac{({y}^{2}+1)({y}^{2}-1)}{y+\frac{1}{y+1}}}\times 23\]
Rewrite \({y}^{2}-1\) in the form \({a}^{2}-{b}^{2}\), where \(a=y\) and \(b=1\).
\[\frac{y}{{y}^{2}-\frac{({y}^{2}+1)({y}^{2}-{1}^{2})}{y+\frac{1}{y+1}}}\times 23\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{y}{{y}^{2}-\frac{({y}^{2}+1)(y+1)(y-1)}{y+\frac{1}{y+1}}}\times 23\]
Simplify \(\frac{({y}^{2}+1)(y+1)(y-1)}{y+\frac{1}{y+1}}\) to \(({y}^{2}+1)(y+1)(y-1)\times \frac{y+1}{y(y+1)+1}\).
\[\frac{y}{{y}^{2}-({y}^{2}+1)(y+1)(y-1)\times \frac{y+1}{y(y+1)+1}}\times 23\]
Expand.
\[\frac{y}{{y}^{2}-({y}^{2}+1)(y+1)(y-1)\times \frac{y+1}{{y}^{2}+y+1}}\times 23\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{y}{{y}^{2}-\frac{({y}^{2}+1)(y+1)(y-1)(y+1)}{{y}^{2}+y+1}}\times 23\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{y}{{y}^{2}-\frac{({y}^{2}+1){(y+1)}^{2}(y-1)}{{y}^{2}+y+1}}\times 23\]
Simplify.
\[\frac{y\times 23}{{y}^{2}-\frac{({y}^{2}+1){(y+1)}^{2}(y-1)}{{y}^{2}+y+1}}\]
Regroup terms.
\[\frac{23y}{{y}^{2}-\frac{({y}^{2}+1){(y+1)}^{2}(y-1)}{{y}^{2}+y+1}}\]
(23*y)/(y^2-((y^2+1)*(y+1)^2*(y-1))/(y^2+y+1))
