Final Answer:
The simplified expression is (11/8)x⁵ - 2x³ - 19.
Step-by-step explanation:
To simplify the given expression (3/8)x⁵ + 15x³ + (1/4)x⁵ - 17x³ - 19, we start by combining like terms. Group the x⁵ terms together and the x³ terms together:
(3/8)x⁵ + (1/4)x⁵ + 15x³ - 17x³ - 19.
Combine the x⁵ terms by adding the coefficients: (3/8 + 1/4)x⁵ = (11/8)x⁵.
Combine the x³ terms by adding the coefficients: 15x³ - 17x³ = -2x³.
Now, the expression becomes (11/8)x⁵ - 2x³ - 19, which is the simplified form.
In this expression, (11/8)x⁵ represents the combined x⁵ terms, -2x³ represents the combined x³ terms, and the constant term -19 remains unchanged. The coefficients are added or subtracted based on their respective terms. This simplification is essential for a clearer and more concise representation of the original expression.