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Katarina [22]
1 year ago
13

If no denominator equals zero , which expression is equivalent to

Mathematics
1 answer:
Scorpion4ik [409]1 year ago
7 0

Answer: Choice D

\frac{-19}{\text{x}-5}

=================================================

Work Shown:

\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}\\\\\\

\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}\\\\\\

This matches with <u>choice D as the final answer.</u>

Keep in mind that we can only subtract fractions when the denominator is the same. The rule is \frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}

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