For x 0, which expression is equivalent to 3x - 2x + 2? | SAT Equivalent expressions Question, Answer Explained

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Math · Advanced MathMedium

For $x > 0$ , which expression is equivalent to $\frac{3}{x} - \frac{2}{x + 2}$ ?

$\frac{1}{2x + 2}$

$\frac{1}{x^2 + 2x}$

$\frac{x + 6}{x^2 + 2x}$

$\frac{5x + 6}{x^2 + 2x}$

Show answer and explanation

Answer: C

Use the common denominator $x(x + 2) = x^2 + 2x$ : $\frac{3(x + 2)}{x(x + 2)} - \frac{2x}{x(x + 2)} = \frac{3x + 6 - 2x}{x^2 + 2x} = \frac{x + 6}{x^2 + 2x}$ .

Choice D adds $2x$ in the numerator instead of subtracting it.

Why the other choices are wrong

A. This subtracts the numerators and adds the denominators. Rewrite both fractions over a common denominator first.
B. This subtracts the original numerators, 3 - 2, without first rewriting each fraction over x(x + 2).
D. This adds 2x to 3x + 6 instead of subtracting it.

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