The least common denominator of the given rational expressions is [tex](x+5)(x-5)^{2}[/tex].
"The least common denominator is the smallest number of all the common multiples of the denominators when 2 or more fractions are given."
The given expressions are:
1. [tex]\frac{1}{x-5}[/tex]
2. [tex]\frac{x+3}{x^{2} -10x+25} = \frac{x+3}{(x-5)^2}[/tex]
3. [tex]\frac{7x}{x^{2} -25} = \frac{7x}{(x+5)(x-5)}[/tex]
Therefore, the least common denominator is
[tex](x+5)(x-5)^{2} = (x+5)(x-5)^{2}[/tex]
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