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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

$the fraction with numerator 1, and denominator x squared, plus 10 x, plus 25, end fraction, equals 4$

If x is a solution to the given equation, which of the following is a possible value of $x plus 5$ ?

ExplanationShow

Choice A is correct. The given equation can be rewritten as $the fraction 1 over, open parenthesis, x plus 5, close parenthesis, squared, end fraction, equals 4$ . Multiplying both sides of this equation by $open parenthesis, x plus 5, close parenthesis, squared$ yields $1 equals, 4 times, open parenthesis, x plus 5, close parenthesis, squared$ . Dividing both sides of this equation by 4 yields $one fourth equals, open parenthesis, x plus 5, close parenthesis, squared$ . Taking the square root of both sides of this equation yields $one half equals, x plus 5$ or $negative one half equals, x plus 5$ . Therefore, a possible value of $x plus 5$ is $one half$ .
Choices B, C, and D are incorrect and may result from computational or conceptual errors.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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