Subtract the polynomials. (Simplify your answer completely.) \[ \left(\frac{3}{8} s^{8}-\frac{3}{4} s^{7}\right)-\left(\frac{1}{3} s^{8}+\frac{1}{5} s^{7}\right) \] SUBMIT ANSWER

To subtract the polynomials, we first need to distribute the negative sign across the second polynomial: \[ \left(\frac{3}{8} s^{8} - \frac{3}{4} s^{7}\right) - \left(\frac{1}{3} s^{8} + \frac{1}{5} s^{7}\right) = \frac{3}{8} s^{8} - \frac{3}{4} s^{7} - \frac{1}{3} s^{8} - \frac{1}{5} s^{7} \] Next, we will combine the like terms (s^8 and s^7 coefficients). For \(s^8\): \[ \frac{3}{8} s^{8} - \frac{1}{3} s^{8} \] To combine these, find a common denominator. The least common multiple of 8 and 3 is 24. Thus, we convert the fractions: \[ \frac{3}{8} = \frac{9}{24}, \quad \frac{1}{3} = \frac{8}{24} \] Now, we can subtract: \[ \frac{9}{24} s^{8} - \frac{8}{24} s^{8} = \frac{1}{24} s^{8} \] For \(s^7\): \[ -\frac{3}{4} s^{7} - \frac{1}{5} s^{7} \] Again, find a common denominator. The least common multiple of 4 and 5 is 20. Therefore, we have: \[ -\frac{3}{4} = -\frac{15}{20}, \quad -\frac{1}{5} = -\frac{4}{20} \] Now, we can combine these: \[ -\frac{15}{20} s^{7} - \frac{4}{20} s^{7} = -\frac{19}{20} s^{7} \] Combining everything together, we have: \[ \frac{1}{24} s^{8} - \frac{19}{20} s^{7} \] So the final simplified answer is: \[ \frac{1}{24} s^{8} - \frac{19}{20} s^{7} \]