Question
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c) For polynomials \( p, q \), and \( r \), where \( (q \neq 0 \) and \( r \neq 0), \frac{p r}{q r} \) simplifies to

Ask by Howell Ross. in the United States
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\(\frac{p r}{q r}\) simplifies to \(\frac{p}{q}\).

Solution

To simplify the expression \(\frac{p r}{q r}\), we can follow these steps: 1. **Identify the common factors**: In the expression \(\frac{p r}{q r}\), both the numerator and the denominator have a common factor of \(r\). 2. **Cancel the common factor**: Since \(r \neq 0\), we can safely cancel \(r\) from both the numerator and the denominator. Thus, we have: \[ \frac{p r}{q r} = \frac{p}{q} \] Therefore, the simplified form of \(\frac{p r}{q r}\) is \(\frac{p}{q}\).

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Bonus Knowledge

When you have the expression \(\frac{p r}{q r}\), you can simplify it by recognizing that the \(r\) in the numerator and the denominator can cancel out, provided \(r \neq 0\). This leaves you with: \[ \frac{p r}{q r} = \frac{p}{q} \] So as long as \(q\) is also not zero ( \(q \neq 0\) ), the expression simplifies beautifully to \(\frac{p}{q}\). Simple, right? But remember, always double-check that neither \(q\) nor \(r\) is zero before going through the swish of cancellation, or you might find yourself in a mathematical mess!

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