To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3x$ and $5x^{2}$ is $15x^{2}$. Multiply $\frac{x+2}{3x}$ times $\frac{5x}{5x}$. Multiply $\frac{x^{2}-2}{5x^{2}}$ times $\frac{3}{3}$.
Since $\frac{\left(x+2\right)\times 5x}{15x^{2}}$ and $\frac{3\left(x^{2}-2\right)}{15x^{2}}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $15x^{2}$ and $9x^{3}$ is $45x^{3}$. Multiply $\frac{8x^{2}+10x-6}{15x^{2}}$ times $\frac{3x}{3x}$. Multiply $\frac{2-x^{3}}{9x^{3}}$ times $\frac{5}{5}$.
Since $\frac{\left(8x^{2}+10x-6\right)\times 3x}{45x^{3}}$ and $\frac{5\left(2-x^{3}\right)}{45x^{3}}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3x$ and $5x^{2}$ is $15x^{2}$. Multiply $\frac{x+2}{3x}$ times $\frac{5x}{5x}$. Multiply $\frac{x^{2}-2}{5x^{2}}$ times $\frac{3}{3}$.
Since $\frac{\left(x+2\right)\times 5x}{15x^{2}}$ and $\frac{3\left(x^{2}-2\right)}{15x^{2}}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $15x^{2}$ and $9x^{3}$ is $45x^{3}$. Multiply $\frac{8x^{2}+10x-6}{15x^{2}}$ times $\frac{3x}{3x}$. Multiply $\frac{2-x^{3}}{9x^{3}}$ times $\frac{5}{5}$.
Since $\frac{\left(8x^{2}+10x-6\right)\times 3x}{45x^{3}}$ and $\frac{5\left(2-x^{3}\right)}{45x^{3}}$ have the same denominator, add them by adding their numerators.
