Final answer:
The expression \(\frac{-7}{5d} + \frac{4}{3d}\) simplifies to \(\frac{-1}{15d}\) after finding a common denominator and combining the terms.
Step-by-step explanation:
To simplify the expression \(\frac{-7}{5d} + \frac{4}{3d}\), we need to find a common denominator and combine the terms. The common denominator for 5d and 3d is 15d. We can rewrite the fractions with the common denominator:
\(\frac{-7}{5d} = \frac{-7 \times 3}{5d \times 3} = \frac{-21}{15d}\)
\(\frac{4}{3d} = \frac{4 \times 5}{3d \times 5} = \frac{20}{15d}\)
Adding the two fractions together we get:
\(\frac{-21 + 20}{15d} = \frac{-1}{15d}\)
No terms can be eliminated further, so \(\frac{-1}{15d}\) is the final, simplified form of the expression. We should then check that this result is reasonable by ensuring that the original fractions were correctly converted to have the same denominator and that the arithmetic was carried out correctly.