To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5x$ and $3y$ is $15xy$. Multiply $\frac{x-1}{5x}$ times $\frac{3y}{3y}$. Multiply $\frac{y-2}{3y}$ times $\frac{5x}{5x}$.
Since $\frac{\left(x-1\right)\times 3y}{15xy}$ and $\frac{\left(y-2\right)\times 5x}{15xy}$ have the same denominator, add them by adding their numerators.
Do the multiplications in $\left(x-1\right)\times 3y+\left(y-2\right)\times 5x$.
$$\frac{3xy-3y+5yx-10x}{15xy}-\frac{xy-1}{2xy}$$
Combine like terms in $3xy-3y+5yx-10x$.
$$\frac{8xy-3y-10x}{15xy}-\frac{xy-1}{2xy}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $15xy$ and $2xy$ is $30xy$. Multiply $\frac{8xy-3y-10x}{15xy}$ times $\frac{2}{2}$. Multiply $\frac{xy-1}{2xy}$ times $\frac{15}{15}$.
Since $\frac{2\left(8xy-3y-10x\right)}{30xy}$ and $\frac{15\left(xy-1\right)}{30xy}$ 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 $5x$ and $3y$ is $15xy$. Multiply $\frac{x-1}{5x}$ times $\frac{3y}{3y}$. Multiply $\frac{y-2}{3y}$ times $\frac{5x}{5x}$.
Since $\frac{\left(x-1\right)\times 3y}{15xy}$ and $\frac{\left(y-2\right)\times 5x}{15xy}$ have the same denominator, add them by adding their numerators.
Do the multiplications in $\left(x-1\right)\times 3y+\left(y-2\right)\times 5x$.
$$\frac{3xy-3y+5yx-10x}{15xy}-\frac{xy-1}{2xy}$$
Combine like terms in $3xy-3y+5yx-10x$.
$$\frac{8xy-3y-10x}{15xy}-\frac{xy-1}{2xy}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $15xy$ and $2xy$ is $30xy$. Multiply $\frac{8xy-3y-10x}{15xy}$ times $\frac{2}{2}$. Multiply $\frac{xy-1}{2xy}$ times $\frac{15}{15}$.
Since $\frac{2\left(8xy-3y-10x\right)}{30xy}$ and $\frac{15\left(xy-1\right)}{30xy}$ have the same denominator, subtract them by subtracting their numerators.
