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Simplify. Express your answer as a single fraction in simplest form. \newline3t−s2\frac{3}{t} - \frac{s}{2}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline3t−s2\frac{3}{t} - \frac{s}{2}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators tt and 22. Since tt is an unknown variable and 22 is a constant, the LCM will be 2t2t.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 22 and the second fraction by tt. This gives us (3×2)/(t×2)−(s×t)/(2×t)(3\times2)/(t\times2) - (s\times t)/(2\times t).
  3. Perform multiplication in numerators and denominators: Perform the multiplication in the numerators and denominators. This results in (6t)−(st2t)(\frac{6}{t}) - (\frac{st}{2t}).
  4. Combine numerators with same denominators: Since the denominators are now the same (2t)(2t), we can combine the numerators. The combined fraction is (6−st)/(2t)(6 - st)/(2t).
  5. Check for further simplification: Check if the fraction can be simplified further. Since 66 and stst do not have common factors and tt is a variable, the fraction is already in simplest form.

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