Question

divide these fractions and select the simplified answer.

9/4x^2/6x/16x^4

A. 9+6x/4x^2+16x^4
B. 3/x
C. 3x
D. x^2/2
E. 6x

Answer 1

To divide the fractions, we start with the expression:

\[
\frac{9}{4x^2} \div \frac{6x}{16x^4}
\]

When dividing by a fraction, we multiply by its reciprocal:

\[
\frac{9}{4x^2} \times \frac{16x^4}{6x}
\]

Now we can simplify the expression before we multiply:

1. Multiply the numerators and denominators:
\[
= \frac{9 \times 16x^4}{4x^2 \times 6x}
\]

2. Simplifying the numerator:
\[
9 \times 16 = 144
\]
So the numerator becomes \(144x^4\).

3. Simplifying the denominator:
\[
4 \times 6 = 24 \quad \text{and} \quad x^2 \times x = 6x^3
\]
So the denominator becomes \(24x^3\).

Thus, we have:

\[
\frac{144x^4}{24x^3}
\]

4. Dividing both the numerator and denominator by 24:
\[
= \frac{144 \div 24}{24 \div 24} \cdot \frac{x^4}{x^3} = \frac{6}{1} \cdot x^{4-3} = 6x
\]

Thus, the simplified answer is:

**E.** 6x