Divide the sum of x^2+4x-1 & 2x-2 by -3x^4
To divide the sum of x^2 + 4x - 1 and 2x - 2 by -3x^4, we can follow these steps:
Step 1: Simplify the sum of x^2 + 4x - 1 and 2x - 2.
Combine like terms:
(x^2 + 4x - 1) + (2x - 2)
= x^2 + 4x - 1 + 2x - 2
= x^2 + 6x - 3
Step 2: Divide the simplified expression by -3x^4.
Divide each term of the expression by -3x^4:
(x^2 + 6x - 3) / -3x^4
Step 3: Express the division as a multiplication by the reciprocal of the denominator.
The division is equivalent to multiplying by the reciprocal of the denominator:
(x^2 + 6x - 3) * (-1 / (3x^4))
Step 4: Simplify the expression.
Multiply each term of the expression by the reciprocal (-1 / (3x^4)):
= (x^2 * (-1 / (3x^4))) + (6x * (-1 / (3x^4))) + (-3 * (-1 / (3x^4)))
= -x^2 / (3x^4) - 6x / (3x^4) + 3 / (3x^4)
Step 5: Further simplify, if possible.
We can simplify by dividing the coefficients and combining the variables with the same exponents:
= -1 / (3x^2) - 2 / (x^3) + 1 / (x^4)
Therefore, the division of the sum of x^2 + 4x - 1 and 2x - 2 by -3x^4 is -1 / (3x^2) - 2 / (x^3) + 1 / (x^4).