We will simplify further as follows:
[tex]\begin{gathered} \frac{1}{\frac{y}{5}-1}=\frac{1}{\frac{y-5}{5}}=\frac{(1)(5)}{(1)(y-5)} \\ \\ =\frac{5}{y-5} \end{gathered}[/tex]
***Sum of fractions***
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]
Now, using this with the information given we have:
[tex]\begin{gathered} \frac{y}{5}-1=\frac{y}{5}-\frac{1}{1}=\frac{(y)(1)-(5)(1)}{(5)(1)} \\ \\ =\frac{y-5}{5} \end{gathered}[/tex]
Now, we know that this expression was the denominator of 1, so:
[tex]\frac{1}{\frac{y}{5}-1}=\frac{1}{\frac{y-5}{5}}[/tex]
Now, using division of fractions
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{(a)(d)}{(b)(c)}[/tex]
So, that is:
[tex]\frac{\frac{1}{1}}{\frac{y-5}{5}}=\frac{(1)(5)}{(1)(y-5)}=\frac{5}{y-5}[/tex]
