divide the polynomialby the monomial denominator by writing the fraction as the sum (or diffrence) of fractions. simplify your answer if possible (-4x+8)/(-4x)
To divide the polynomial (-4x + 8) by the monomial denominator (-4x), we can write it as the sum (or difference) of fractions.
First, we break down the polynomial into two terms: -4x and 8.
Then, we represent each term as a fraction with the monomial denominator -4x:
(-4x + 8)/(-4x) = (-4x)/(-4x) + 8/(-4x)
The first term simplifies to 1 since -4x divided by -4x equals 1:
(-4x)/(-4x) = 1
Therefore, the expression becomes:
1 + 8/(-4x)
Further simplifying, we can divide 8 by -4 to get -2:
1 + (-2/x) = 1 - (2/x)
So, the final simplified expression is 1 - (2/x).