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domain \( \frac{9 x+1}{x-5}=\frac{18 x+7}{2 x-7} \)

Ask by Mcfarlane Wang. in the United States
Feb 22,2025

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The solutions are \( x = -\frac{14}{11} \) and \( x = -1.2727 \).

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To find the domain of the expression, we need to ensure that the denominators do not equal zero. Set each denominator equal to zero: 1. For \( x - 5 = 0 \) → \( x \neq 5 \) 2. For \( 2x - 7 = 0 \) → \( x \neq \frac{7}{2} \) Thus, the domain of the expression is all real numbers except \( x = 5 \) and \( x = \frac{7}{2} \). So, the domain in interval notation is \( (-\infty, \frac{7}{2}) \cup (\frac{7}{2}, 5) \cup (5, \infty) \). Enjoy solving and remember: identify restrictions on variables right from the start!

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