Question

find the difference.
\\(\frac{9}{3x} - \frac{4}{2x^2}\\)
\\(\bigcirc\\) a. \\(\frac{1}{x}\\)
\\(\bigcirc\\) b. \\(\frac{5}{3x - 2x^2}\\)
\\(\bigcirc\\) c. \\(\frac{18x - 12}{5x^2}\\)
\\(\bigcirc\\) d. \\(\frac{3x - 2}{x^2}\\)

Explanation:

Step1: Simplify the first fraction

Simplify \(\frac{9}{3x}\) to \(\frac{3}{x}\).

Step2: Find a common denominator

The denominators are \(x\) and \(2x^2\), so the common denominator is \(2x^2\). Rewrite \(\frac{3}{x}\) with the common denominator: \(\frac{3\times2x}{x\times2x}=\frac{6x}{2x^2}\).

Step3: Subtract the fractions

Now subtract \(\frac{4}{2x^2}\) from \(\frac{6x}{2x^2}\): \(\frac{6x - 4}{2x^2}\).

Step4: Factor the numerator

Factor out a 2 from the numerator: \(\frac{2(3x - 2)}{2x^2}\).

Step5: Simplify the fraction

Cancel out the common factor of 2: \(\frac{3x - 2}{x^2}\).

Answer:

D. \(\frac{3x - 2}{x^2}\)