Answer
The required expression is $\underline{\frac{\left( x+1 \right)}{\left( x-5 \right)}}$
Work Step by Step
Let us consider the given polynomial:
$\frac{{{x}^{2}}+6x+5}{{{x}^{2}}-25}$ ……………….….. (1)
Apply the technique ‘‘factoring the polynomial completely’’ and factor the denominator by ‘‘factoring the difference of two squares’’.
$\begin{align}
& \frac{{{x}^{2}}+6x+5}{{{x}^{2}}-25}=\frac{{{x}^{2}}+5x+x+5}{{{x}^{2}}-{{5}^{2}}} \\
& =\frac{x\left( x+5 \right)+1\left( x+5 \right)}{\left( x+5 \right)\left( x-5 \right)} \\
& =\frac{\left( x+1 \right)\left( x+5 \right)}{\left( x+5 \right)\left( x-5 \right)}
\end{align}$
Solve further,
$\frac{{{x}^{2}}+6x+5}{{{x}^{2}}-25}=\frac{\left( x+1 \right)}{\left( x-5 \right)}$
