Question
Part 2 of 2 , Given polynomials \( p, q, r \), and \( s \) such that \( q \neq 0, r \neq 0 \), and \( s \neq 0, \frac{p}{q} \div \frac{r}{s}= \) ?
Ask by Alexander Ward. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression simplifies to \( \frac{p \cdot s}{q \cdot r} \).
Solution
To solve the expression \( \frac{p}{q} \div \frac{r}{s} \), we can follow these steps:
1. **Understand the Division of Fractions**: Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression as:
\[
\frac{p}{q} \div \frac{r}{s} = \frac{p}{q} \times \frac{s}{r}
\]
2. **Multiply the Fractions**: When multiplying fractions, we multiply the numerators together and the denominators together:
\[
\frac{p}{q} \times \frac{s}{r} = \frac{p \cdot s}{q \cdot r}
\]
Thus, the final result of the expression \( \frac{p}{q} \div \frac{r}{s} \) is:
\[
\frac{p \cdot s}{q \cdot r}
\]
This is the simplified form of the given expression.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To solve \(\frac{p}{q} \div \frac{r}{s}\), we can rewrite the division of fractions as multiplication by the reciprocal. This means we can express it as \(\frac{p}{q} \times \frac{s}{r}\). By multiplying the numerators and the denominators together, we get: \[ \frac{p \cdot s}{q \cdot r} \] This is your final result, and it combines all the elements in a neat and simplified fraction! Now, while dealing with polynomials, remember that you can often factor them for simplification before performing operations. Common mistakes include forgetting to check for common factors or cancellations when multiplying or dividing. Always double-check your work for any simplifications!
