Question

fa25 math 125 - 09: precalculus i homework: ch 1.2 operations with algebraic expressions question 15, ar.3.83 hw score: 77.78%, 14 of 18 points o points: 0 of 1 divide. $\frac{30m^{2}n^{2}-8mn^{3}+18m^{2}n}{6m^{2}n}$ (simplify your answer.) question list question 14 question 15 question 16 question 17 question 18 get more help -

Explanation:

Step1: Split into three fractions

$\frac{30m^{2}n^{2}-8mn^{3}+18m^{2}n}{6m^{2}n}=\frac{30m^{2}n^{2}}{6m^{2}n}-\frac{8mn^{3}}{6m^{2}n}+\frac{18m^{2}n}{6m^{2}n}$

Step2: Simplify each fraction

• For $\frac{30m^{2}n^{2}}{6m^{2}n}$, divide coefficients and subtract exponents: $\frac{30}{6}m^{2 - 2}n^{2-1}=5n$.
• For $\frac{8mn^{3}}{6m^{2}n}$, $\frac{8}{6}m^{1 - 2}n^{3 - 1}=\frac{4}{3}m^{-1}n^{2}=\frac{4n^{2}}{3m}$.
• For $\frac{18m^{2}n}{6m^{2}n}$, $\frac{18}{6}m^{2-2}n^{1 - 1}=3$.

Answer:

$5n-\frac{4n^{2}}{3m}+3$