To divide fractions, we use the concept of multiplying by the reciprocal. Let's break it down step by step:
Given:
\[ \frac{3}{4} \div \frac{12}{2x + 6} \]
**Step 1: Write the Reciprocal**
The reciprocal of \(\frac{12}{2x + 6}\) is \(\frac{2x + 6}{12}\). So the problem now becomes:
\[ \frac{3}{4} \times \frac{2x + 6}{12} \]
**Step 2: Multiply the Fractions**
Multiply the numerators together and the denominators together:
\[ \frac{3 \times (2x + 6)}{4 \times 12} = \frac{3(2x + 6)}{48} \]
**Step 3: Simplify**
First, simplify the numerator and the denominator.
The numerator \(3(2x + 6)\) can be expanded:
\[ 3(2x + 6) = 6x + 18 \]
The fraction now looks like this:
\[ \frac{6x + 18}{48} \]
Next, we can simplify both the numerator and the denominator by dividing by their greatest common divisor (GCD). The GCD of 6x + 18 and 48 is 6.
So, divide numerator and denominator by 6:
\[ \frac{6x + 18}{48} = \frac{6(x + 3)}{48} = \frac{x + 3}{8} \]
The simplified form of the given expression \(\frac{3}{4} \div \frac{12}{2x + 6}\) is:
\[ \frac{x + 3}{8} \]
divide these fractions and simplify the answer.
3/4 divided by 12/2x+6
1 answer