Question

divide
\\(\frac{12x^2 - 13x}{2x}\\)
simplify your answer as much as possible

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{12x^2 - 13x}{2x}\) into two separate fractions: \(\frac{12x^2}{2x}-\frac{13x}{2x}\)

Step2: Simplify each fraction

For the first fraction \(\frac{12x^2}{2x}\), we can simplify the coefficients and the variables separately. The coefficient part: \(\frac{12}{2} = 6\), and the variable part: \(\frac{x^2}{x}=x\) (using the rule \(x^a\div x^b = x^{a - b}\), here \(a = 2\), \(b=1\), so \(x^{2-1}=x\)). So \(\frac{12x^2}{2x}=6x\)

For the second fraction \(\frac{13x}{2x}\), the \(x\) terms cancel out (since \(x\div x = 1\) for \(x
eq0\)), so we are left with \(\frac{13}{2}\)

Step3: Combine the results

Combining the two simplified fractions, we get \(6x-\frac{13}{2}\)

Answer:

\(6x - \frac{13}{2}\)