Answer: Choice D
[tex]\frac{-19}{\text{x}-5}[/tex]
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Work Shown:
[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]
[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]
This matches with choice D as the final answer.
Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]