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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.

If u minus 3 equals, the fraction 6 over, t minus 2, end fraction , what is t in terms of u ?

ExplanationShow

Choice D is correct. Multiplying both sides of the given equation by t minus 2 yields open parenthesis, t minus 2, close parenthesis, times, open parenthesis, u minus 3, close parenthesis, equals 6. Dividing both sides of this equation by u minus 3 yields t minus 2, equals, the fraction with numerator 6, and denominator u minus 3, end fraction. Adding 2 to both sides of this equation yields t equals, the fraction with numerator 6, and denominator u minus 3, end fraction, plus 2, which can be rewritten as t equals, the fraction with numerator 6, and denominator u minus 3, end fraction, plus, the fraction with numerator 2 times, open parenthesis, u minus 3, close parenthesis, and denominator u minus 3, end fraction. Since the fractions on the right-hand side of this equation have a common denominator, adding the fractions yields t equals, the fraction with numerator 6 plus 2, times, open parenthesis, u minus 3, close parenthesis, and denominator u minus 3, end fraction. Applying the distributive property to the numerator on the right-hand side of this equation yields t equals, the fraction with numerator 6 plus 2 u, minus 6, and denominator u minus 3, end fraction, which is equivalent to t equals, the fraction with numerator 2 u, and denominator u minus 3, end fraction.

Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.

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