Which expression is equivalent to \dfrac{x}{x - 1} - \dfrac{1}{x + 2}?

\dfrac{x^2 + x + 1}{(x-1)(x+2)} Common denominator: \dfrac{x(x+2) - (x-1)}{(x-1)(x+2)} = \dfrac{x^2 + 2x - x + 1}{(x-1)(x+2)} = \dfrac{x^2 + x + 1}{(x-1)(x+2)}.

\dfrac{x^2 + 2x + 1}{(x-1)(x+2)}

Equivalent Expressions

SAT Math· difficulty 4/5

\dfrac{x}{x - 1} - \dfrac{1}{x + 2}

A
$\dfrac{x - 1}{(x-1)(x+2)}$
B
$\dfrac{x^2 + 2x + 1}{(x-1)(x+2)}$
C
$\dfrac{x^2 - 1}{(x-1)(x+2)}$
D
$\dfrac{x^2 + x + 1}{(x-1)(x+2)}$
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Explanation

\dfrac{x(x+2) - (x-1)}{(x-1)(x+2)} = \dfrac{x^2 + 2x - x + 1}{(x-1)(x+2)} = \dfrac{x^2 + x + 1}{(x-1)(x+2)}

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