Question

divide.
\\(\dfrac{9m^3 + 12m^2 + 18m}{3m^3}\\)

Explanation:

Step1: Split the fraction

Split the numerator into three separate fractions: $\frac{9m^3}{3m^3} + \frac{12m^2}{3m^3} + \frac{18m}{3m^3}$

Step2: Simplify each fraction

• For the first term: $\frac{9m^3}{3m^3} = 3$ (divide coefficients and subtract exponents of like bases: $9\div3 = 3$, $m^3\div m^3 = m^{3 - 3}=m^0 = 1$)
• For the second term: $\frac{12m^2}{3m^3}=\frac{12}{3}\times\frac{m^2}{m^3}=4\times m^{2 - 3}=4m^{-1}=\frac{4}{m}$ (divide coefficients, subtract exponents of $m$)
• For the third term: $\frac{18m}{3m^3}=\frac{18}{3}\times\frac{m}{m^3}=6\times m^{1 - 3}=6m^{-2}=\frac{6}{m^2}$ (divide coefficients, subtract exponents of $m$)

Step3: Combine the simplified terms

Combine the three simplified terms: $3+\frac{4}{m}+\frac{6}{m^2}$

Answer:

$3 + \frac{4}{m} + \frac{6}{m^2}$