13) (3 x)/(5 x+5 y)-(x)/(10 x-10 y)

1. **Factor out common terms:**<br /> $\frac{3x}{2(4x+3y)} - \frac{x}{10(x-y)}$<br /><br />2. **Find a common denominator:** The common denominator is $10(x-y)(4x+3y)$.<br /><br />3. **Rewrite fractions with the common denominator:**<br /> $\frac{3x \cdot 5(x-y)}{10(4x+3y)(x-y)} - \frac{x \cdot (4x+3y)}{10(x-y)(4x+3y)}$<br /><br />4. **Combine the numerators:**<br /> $\frac{15x(x-y) - x(4x+3y)}{10(x-y)(4x+3y)}$<br /><br />5. **Expand and simplify the numerator:**<br /> $\frac{15x^2 - 15xy - 4x^2 - 3xy}{10(x-y)(4x+3y)} = \frac{11x^2 - 18xy}{10(x-y)(4x+3y)}$<br /><br />6. **Factor out x from the numerator (optional, depending on desired form):**<br /> $\frac{x(11x - 18y)}{10(x-y)(4x+3y)}$<br />