Question

question
simplify: \\(\frac{18p^2 - 24p}{-3p}\\)

Explanation:

Step1: Factor numerator

Factor out \(6p\) from \(18p^2 - 24p\), we get \(6p(3p - 4)\). So the expression becomes \(\frac{6p(3p - 4)}{-3p}\).

Step2: Cancel common terms

Cancel out the common factor \(3p\) from numerator and denominator. \(6p\div3p = 2\), and we have a negative sign from the denominator. So we get \(-2(3p - 4)\).

Step3: Distribute the -2

Distribute \(-2\) to \(3p\) and \(-4\), we get \(-6p + 8\) or we can also simplify the fraction directly by dividing each term in the numerator by the denominator: \(\frac{18p^2}{-3p}-\frac{24p}{-3p}\). For \(\frac{18p^2}{-3p}\), divide coefficients \(18\div(-3)= - 6\) and subtract exponents of \(p\) (\(p^2\div p = p\)), so it's \(-6p\). For \(\frac{24p}{-3p}\), divide coefficients \(24\div(-3)= - 8\) but there are two negative signs so it's \(+8\). So combining we get \(-6p + 8\).

Answer:

\(-6p + 8\)