Answer:
The value of [tex]\frac{\left(\frac{y}{5}\right)+1}{\left(\frac{y^{2}}{25}\right)-1}=\frac{5}{y-5}[/tex]
Solution:
As given, [tex]\frac{\left(\frac{y}{5}\right)+1}{\left(\frac{y^{2}}{25}\right)-1}[/tex]
[tex]\frac{\left(\frac{y}{5}\right)+1}{\left(\frac{y}{5}\right)^{2}-1^{2}}[/tex]
[tex]\frac{\frac{y}{5}+1}{\left(\frac{y}{5}+1\right) \times\left(\frac{y}{5}-1\right)}[/tex]
as we know [tex]\left(a^{2}-b^{2}\right)=(a+b)\times(a-b)[/tex]
This can be written as,
[tex]\Rightarrow \frac{\frac{y}{5}+1}{\frac{y}{5}+1} \times \frac{1}{\frac{y}{5}-1}[/tex]
Because [tex]\Rightarrow \frac{\frac{y}{5}+1}{\frac{y}{5}+1}=1[/tex]
[tex]\Rightarrow 1 \times \frac{1}{\frac{y}{5}-1} = \frac{5}{y-5}[/tex]
