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12) \( \frac{1}{3 z}+\frac{1}{2}=\frac{5}{2 z}-\frac{1}{z} \)

Ask by Turner Garrett. in Argentina
Jan 21,2025

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La solución es \( z = \frac{7}{3} \).

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To solve the equation \( \frac{1}{3 z}+\frac{1}{2}=\frac{5}{2 z}-\frac{1}{z} \), first, we need to eliminate the fractions by finding a common denominator. The common denominator for \( z \) in this case is \( 6z \). Multiply both sides of the equation by \( 6z \) to get: \[ 6z \left( \frac{1}{3z} \right) + 6z \left( \frac{1}{2} \right) = 6z \left( \frac{5}{2z} \right) - 6z \left( \frac{1}{z} \right) \] This simplifies to: \[ 2 + 3z = 15 - 6 \] Combining like terms: \[ 2 + 3z = 15 - 6 \implies 3z = 9 \implies z = 3 \] Therefore, the solution is \( z = 3 \).

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