divide these fractions and select the simplified answer.

Question

4/2x+2/8/3x+3
Invert the bottom fraction and multiply it by the top fraction.
A. 3x+3/2x+4
B. 3/4
C. 12/5x+5
D. 3/16
E. 3/2

Answer 1

Let's tackle the problem step by step:

Given the expression to divide:
\[
\frac{4}{2x+2} \div \frac{8}{3x+3}
\]

1. Invert the second fraction (the divisor):
\[
\frac{4}{2x+2} \times \frac{3x+3}{8}
\]

2. Simplify the terms as much as possible:
- \(2x+2\) can be factored as \(2(x+1)\),
- \(3x+3\) can be factored as \(3(x+1)\).

Thus, the multiplication becomes:
\[
\frac{4}{2(x+1)} \times \frac{3(x+1)}{8}
\]

3. Cancel out the common terms \((x+1)\):
\[
\frac{4}{2} \times \frac{3}{8}
\]

4. Simplify the fractions:
\[
\frac{4}{2} = 2 \quad \text{and} \quad \frac{3}{8} = \frac{3}{8}
\]

5. Multiply the simplified fractions together:
\[
2 \times \frac{3}{8} = \frac{6}{8} = \frac{3}{4}
\]

So, the simplified answer is:

B. \(\frac{3}{4}\)