Question

Can someone help me

Answer 1

Answer: Choice B

All real numbers except 2 and 5

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Explanation:

Factor the denominator.  We need to find two numbers that multiply to 10 and add to -7.

Through trial and error, those two numbers are -2 and -5

-2 times -5 = 10

-2 plus -5 = -7

This means the denominator $\text{x}^2 - 7\text{x} + 10$ factors to $(\text{x}-2)(\text{x}-5)$. You can use the FOIL rule to confirm this.

Then each piece is set equal to zero to solve for x

x-2 = 0 leads to x = 2

x-5 = 0 leads to x = 5

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In short, if x = 2 or x = 5, then it causes the the denominator $\text{x}^2 -7\text{x}+10$ to turn into 0.

Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.