Answer
$\frac{(x-5)}{2}; x \ne 1,-5;$
Work Step by Step
$\frac{(x^{2}-25)}{(2x-2)} \div \frac{x^{2}+10x+25}{x^{2}+4x-5}$
Factor numerator and denominator.
$=\frac{(x+5)(x-5)}{2(x-1)} \div \frac{(x+5)(x+5)}{(x+5)(x-1)}$
Exclude the numbers 1 and -5 for $x$ for non-zero denominators.
$=\frac{(x+5)(x-5)}{2(x-1)} \div \frac{(x+5)(x+5)}{(x+5)(x-1)} ; x \ne 1,-5;$
Invert the divisor and multiply.
$=\frac{(x+5)(x-5)}{2(x-1)} \times \frac{(x+5)(x-1)}{(x+5)(x+5)} ; x \ne 1,-5;$
Divide common factors
$=\frac{(x-5)}{2}; x \ne 1,-5;$
