Question

select the correct answer.
what is the quotient?
\\(\frac{15x^2 - 10}{5x}\\)
\\(\bigcirc\\) a. \\(3x^2 - 2\\)
\\(\bigcirc\\) b. \\(\frac{3x - 2}{x}\\)
\\(\bigcirc\\) c. \\(\frac{3x^2 - 2}{5}\\)
\\(\bigcirc\\) d. \\(\frac{3x^2 - 2}{x}\\)

Explanation:

Step1: Split the fraction

We can split the fraction \(\frac{15x^{2}-10}{5x}\) into two separate fractions: \(\frac{15x^{2}}{5x}-\frac{10}{5x}\).

Step2: Simplify each fraction

For the first fraction \(\frac{15x^{2}}{5x}\), we divide the coefficients and subtract the exponents of \(x\) (using the rule \(\frac{x^{m}}{x^{n}} = x^{m - n}\)). So, \(\frac{15}{5}=3\) and \(x^{2-1}=x\), thus \(\frac{15x^{2}}{5x}=3x\).
For the second fraction \(\frac{10}{5x}\), we simplify the coefficient: \(\frac{10}{5} = 2\), so \(\frac{10}{5x}=\frac{2}{x}\).

Step3: Combine the simplified fractions

Now we have \(3x-\frac{2}{x}\). To combine these into a single fraction, we find a common denominator (which is \(x\)): \(\frac{3x\cdot x}{x}-\frac{2}{x}=\frac{3x^{2}-2}{x}\).

Answer:

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