Discussion

If \( a = 3 \), \( b = 2 \), \( c = 4 \) and \( x = 5 \), then the value of \( \dfrac{4ab - 2acx}{2ab + 3ac} \) is

Answer: A

Evaluate the numerator and denominator separately.

\[ 4ab = 4 \times 3 \times 2 = 24 \]

\[ 2acx = 2 \times 3 \times 4 \times 5 = 120 \]

\[ \text{numerator} = 24 - 120 = -96 \]

\[ 2ab = 12, \qquad 3ac = 36 \quad\Longrightarrow\quad \text{denominator} = 48 \]

\[ \frac{-96}{48} = -2 \]

Substituting into the whole numerator before dividing avoids the common error of cancelling term by term.

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