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Simplify. Express your answer as a single fraction in simplest form. \newline5w−32\frac{5}{w} - \frac{3}{2}

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5w−32\frac{5}{w} - \frac{3}{2}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators ww and 22. Since ww is a variable and 22 is a constant, the LCM is simply 2w2w.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 22\frac{2}{2} and the second fraction by ww\frac{w}{w}. This gives us 5×2w×2−3×w2×w\frac{5\times 2}{w\times 2} - \frac{3\times w}{2\times w}.
  3. Perform multiplication: Perform the multiplication in the numerators and denominators. This results in (102w)−(3w2w)(\frac{10}{2w}) - (\frac{3w}{2w}).
  4. Simplify the expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (10−3w)/(2w)(10 - 3w)/(2w).

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