$$\frac{ 2 }{ { m }^{ 3 } n } + \frac{ 5 }{ { m }^{ 2 } { n }^{ 2 } } - \frac{ 10 }{ m { n }^{ 3 } }$$
Evaluate
$\frac{2n^{2}+5mn-10m^{2}}{\left(mn\right)^{3}}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $m^{3}n$ and $m^{2}n^{2}$ is $n^{2}m^{3}$. Multiply $\frac{2}{m^{3}n}$ times $\frac{n}{n}$. Multiply $\frac{5}{m^{2}n^{2}}$ times $\frac{m}{m}$.
Since $\frac{2n}{n^{2}m^{3}}$ and $\frac{5m}{n^{2}m^{3}}$ have the same denominator, add them by adding their numerators.
$$\frac{2n+5m}{n^{2}m^{3}}-\frac{10}{mn^{3}}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $n^{2}m^{3}$ and $mn^{3}$ is $m^{3}n^{3}$. Multiply $\frac{2n+5m}{n^{2}m^{3}}$ times $\frac{n}{n}$. Multiply $\frac{10}{mn^{3}}$ times $\frac{m^{2}}{m^{2}}$.
Since $\frac{\left(2n+5m\right)n}{m^{3}n^{3}}$ and $\frac{10m^{2}}{m^{3}n^{3}}$ have the same denominator, subtract them by subtracting their numerators.
