Question
divide these fractions and simplify the answer.
25/4x/10x^2/8x^4
25/4x/10x^2/8x^4
Answers
Answered by
GPT-4o mini
To divide the fractions \(\frac{25}{4x}\) by \(\frac{10x^2}{8x^4}\), we can multiply by the reciprocal of the second fraction.
Here’s how you can do it step by step:
1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{25}{4x} \div \frac{10x^2}{8x^4} = \frac{25}{4x} \times \frac{8x^4}{10x^2}
\]
2. Multiply the numerators and the denominators:
\[
= \frac{25 \times 8x^4}{4x \times 10x^2}
\]
3. Simplifying the numerators and denominators:
\[
= \frac{200x^4}{40x^3}
\]
4. Now simplify the fraction \( \frac{200}{40} \) and \( \frac{x^4}{x^3} \):
\[
= \frac{200 \div 40}{40 \div 40} \frac{x^4}{x^3} = \frac{5}{1} x^{4-3} = 5x
\]
Thus, the simplified result of dividing the fractions is:
\[
\boxed{5x}
\]
Here’s how you can do it step by step:
1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{25}{4x} \div \frac{10x^2}{8x^4} = \frac{25}{4x} \times \frac{8x^4}{10x^2}
\]
2. Multiply the numerators and the denominators:
\[
= \frac{25 \times 8x^4}{4x \times 10x^2}
\]
3. Simplifying the numerators and denominators:
\[
= \frac{200x^4}{40x^3}
\]
4. Now simplify the fraction \( \frac{200}{40} \) and \( \frac{x^4}{x^3} \):
\[
= \frac{200 \div 40}{40 \div 40} \frac{x^4}{x^3} = \frac{5}{1} x^{4-3} = 5x
\]
Thus, the simplified result of dividing the fractions is:
\[
\boxed{5x}
\]