$$\frac{ 2-x }{ x } - \frac{ x+5 }{ { x }^{ 2 } +1 }$$
Evaluate
$\frac{2-6x+x^{2}-x^{3}}{x\left(x^{2}+1\right)}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x$ and $x^{2}+1$ is $x\left(x^{2}+1\right)$. Multiply $\frac{2-x}{x}$ times $\frac{x^{2}+1}{x^{2}+1}$. Multiply $\frac{x+5}{x^{2}+1}$ times $\frac{x}{x}$.
Since $\frac{\left(2-x\right)\left(x^{2}+1\right)}{x\left(x^{2}+1\right)}$ and $\frac{\left(x+5\right)x}{x\left(x^{2}+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x$ and $x^{2}+1$ is $x\left(x^{2}+1\right)$. Multiply $\frac{2-x}{x}$ times $\frac{x^{2}+1}{x^{2}+1}$. Multiply $\frac{x+5}{x^{2}+1}$ times $\frac{x}{x}$.
Since $\frac{\left(2-x\right)\left(x^{2}+1\right)}{x\left(x^{2}+1\right)}$ and $\frac{\left(x+5\right)x}{x\left(x^{2}+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
