Problem

Divide the expression \(\frac{6x^2 - 5x - 1}{3x + 2}\) by \(2x - 1\).

Answer

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Answer

This simplifies to \(\frac{6x^2 - 5x - 1}{3x + 2}\).

Steps

Step 1 ：First, we divide the numerator and denominator of the first fraction by \(2x - 1\): \(\frac{6x^2 - 5x - 1}{2x - 1}\) divided by \(\frac{3x + 2}{2x - 1}\).

Step 2 ：In order to divide by a fraction, we multiply by its reciprocal. Thus, we get \(\frac{6x^2 - 5x - 1}{2x - 1} \times \frac{2x - 1}{3x + 2}\).

Step 3 ：This simplifies to \(\frac{6x^2 - 5x - 1}{3x + 2}\).

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