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Simplify. Express your answer as a single fraction in simplest form. \newlinez2−35yz\frac{z}{2} - \frac{3}{5yz}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinez2−35yz\frac{z}{2} - \frac{3}{5yz}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 22 and 5yz5yz. Since 22 and 5yz5yz have no common factors other than 11, the LCM is simply their product, which is 10yz10yz.
  2. Make Denominators Same: Make the denominators the same by multiplying the first fraction by 5yz5yz\frac{5yz}{5yz} and the second fraction by 22\frac{2}{2}. This gives us 5yz⋅z10yz−610yz\frac{5yz\cdot z}{10yz} - \frac{6}{10yz}.
  3. Simplify Expression: Simplify the expression by combining the numerators since the denominators are the same. The final simplified expression is (5yz⋅z−610yz)(\frac{5yz\cdot z - 6}{10yz}).
  4. Check for Further Simplification: Check if the expression can be simplified further. Since there are no common factors between the numerator and the denominator, the expression is already in its simplest form.

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