Simplify by removing factors of 1 . \( \frac{6 r+30}{r^{2}-r-30} \) The simplified form is \( \square \)
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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 \( \frac{6}{r - 6} \).