Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. −4x^2−2x+3/−2x
To divide the polynomial by the monomial denominator, we can write the fraction as the sum (or difference) of fractions with the same denominator.
Start by expressing the numerator, −4x^2 − 2x + 3, as the sum of two fractions:
−4x^2 − 2x + 3 = (-4x^2)/(-2x) + (-2x)/(-2x) + 3/(-2x)
Now simplify each fraction separately:
(-4x^2)/(-2x) = 2x
(-2x)/(-2x) = 1
3/(-2x) = -3/(2x)
Combine the simplified fractions back together:
(-4x^2 − 2x + 3)/(-2x) = 2x + 1 - (3/(2x))
Therefore, the simplified form of the fraction is 2x + 1 - (3/(2x)).