Questions: Simplify the expression by dividing the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. (6x+12)/(-6)

$Simplify the expression by dividing the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. (6x+12)/(-6)$

Transcript text: Simplify the expression by dividing the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. \[ \frac{6 x+12}{-6} \]

Solution

Solution Steps

To solve the given problem, we need to divide the polynomial in the numerator by the monomial in the denominator. This can be done by splitting the fraction into two separate fractions and then simplifying each one individually.

Solution Approach

Split the fraction $\frac{6x + 12}{-6}$ into two separate fractions: $\frac{6x}{-6}$ and $\frac{12}{-6}$.
Simplify each fraction individually.
Combine the simplified results to get the final answer.

Step 1: Split the Fraction

We start by splitting the fraction $\frac{6x + 12}{-6}$ into two separate fractions: \[ \frac{6x + 12}{-6} = \frac{6x}{-6} + \frac{12}{-6} \]

Step 2: Simplify Each Fraction

Next, we simplify each fraction individually: \[ \frac{6x}{-6} = -1x = -x \] \[ \frac{12}{-6} = -2 \]

Step 3: Combine the Simplified Results

Finally, we combine the simplified results to get the final expression: \[ -x - 2 \]