Final answer:
The expression is simplified by combining like terms and organizing in descending powers of x, resulting in a polynomial – not a fraction – in the form of -5x⁶ + x³ + x² - 10x + 21.
Step-by-step explanation:
To express the given expression as a single fraction in the form ax + b + cx² + dx⁴ where a, b, c, and d are integers, we first need to combine like terms.
Given expression: x - 2 + x² - 5x⁶ + x³ + 23 - 9x. Let's organize the terms in descending powers of x. This gives us -5x⁶ + x³ + x² - (9x + x) - 2 + 23.
Next, we combine the like terms, specifically the terms with x and the constant terms. The x terms combine to -10x, and the constant terms combine to 21.
Our final expression is -5x⁶ + x³ + x² - 10x + 21. This is already in the form of a polynomial, not a fraction. There's no denominator to form a fraction, so the expression as provided is in its simplest form.