Question
Simplify by removing factors of 1 . \( \frac{6 r+30}{r^{2}-r-30} \) The simplified form is \( \square \)
Ask by Boone Thornton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{6}{r-6} \).
Solution
Calculate or simplify the expression \( \frac{6r+30}{r^{2}-r-30} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{6r+30}{r^{2}-r-30}\)
- step1: Factor the expression:
\(\frac{6\left(r+5\right)}{\left(r+5\right)\left(r-6\right)}\)
- step2: Reduce the fraction:
\(\frac{6}{r-6}\)
The simplified form of \( \frac{6 r+30}{r^{2}-r-30} \) is \( \frac{6}{r-6} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify \( \frac{6r + 30}{r^{2} - r - 30} \), we can factor both the numerator and the denominator. The numerator \( 6r + 30 \) can be factored as \( 6(r + 5) \). Now, let's factor the denominator \( r^{2} - r - 30 \). We need two numbers that multiply to -30 and add to -1. Those numbers are -6 and 5, so we can factor it as \( (r - 6)(r + 5) \). Now, substituting these factors into the fraction, we have: \[ \frac{6(r + 5)}{(r - 6)(r + 5)} \] Next, we can cancel out the common factor \( (r + 5) \) from the numerator and the denominator. This gives us: \[ \frac{6}{r - 6} \] Thus, the simplified form is \( \frac{6}{r - 6} \).
