Cancel out $x-2$ in both numerator and denominator.
$$\frac{x+3}{x}+\frac{x+1}{x+2}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x$ and $x+2$ is $x\left(x+2\right)$. Multiply $\frac{x+3}{x}$ times $\frac{x+2}{x+2}$. Multiply $\frac{x+1}{x+2}$ times $\frac{x}{x}$.
Since $\frac{\left(x+3\right)\left(x+2\right)}{x\left(x+2\right)}$ and $\frac{\left(x+1\right)x}{x\left(x+2\right)}$ have the same denominator, add them by adding their numerators.
Cancel out $x-2$ in both numerator and denominator.
$$\frac{x+3}{x}+\frac{x+1}{x+2}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x$ and $x+2$ is $x\left(x+2\right)$. Multiply $\frac{x+3}{x}$ times $\frac{x+2}{x+2}$. Multiply $\frac{x+1}{x+2}$ times $\frac{x}{x}$.
Since $\frac{\left(x+3\right)\left(x+2\right)}{x\left(x+2\right)}$ and $\frac{\left(x+1\right)x}{x\left(x+2\right)}$ have the same denominator, add them by adding their numerators.
