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Simplify. Express your answer as a single fraction in simplest form. \newline5v−uv4\frac{5}{v} - \frac{uv}{4}

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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. \newline5v−uv4\frac{5}{v} - \frac{uv}{4}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators vv and 44. Since vv is a variable and 44 is a constant, the LCM is simply 4v4v.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 44\frac{4}{4} and the second fraction by vv\frac{v}{v}. This gives us 5×4v×4−uv×v4×v\frac{5\times 4}{v\times 4} - \frac{uv\times v}{4\times v}.
  3. Perform multiplication in numerators and denominators: Perform the multiplication in the numerators and denominators. This results in 204v−uv24v\frac{20}{4v} - \frac{uv^2}{4v}.
  4. Simplify the expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (20−uv2)/4v(20 - uv^2)/4v.

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