Final answer:
To find the result of the subtraction, subtract corresponding terms and combine like terms. The result is -2x^4 + 3x^3 - 8x^2 - 1/6x - 7.
Step-by-step explanation:
The question asks us to find the result of subtracting the expression (11x^4 - 9 - 4x^2 - 5/6x) from (9x^4 - 3x^3 + 4x^2 - 7/6x - 7).
To approach this problem, we subtract each corresponding term in the second expression from the first, taking special care with the coefficients and the signs. We can line up the terms according to their degree. Then, we simply subtract the coefficients remembering that subtracting a negative is equivalent to adding a positive.
Here's the step-by-step breakdown:
- Subtract the x^4 terms: 9x^4 - 11x^4 = -2x^4.
- Subtract the x^3 terms, noting that there is no x^3 term in the expression to be subtracted, so we simply bring down the -3x^3 term.
- Subtract the x^2 terms: 4x^2 - (-4x^2) = 4x^2 + 4x^2 = 8x^2.
- Subtract the x terms: -7/6x - (-5/6x) = -7/6x + 5/6x = -1/6x.
- Finally, bring down the constant term -7 as there is no constant term in the expression to be subtracted.
Putting it all together, the result is: -2x^4 + 3x^3 - 8x^2 - 1/6x - 7.