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Simplify. Express your answer as a single fraction in simplest form. \newline4uv+uv5\frac{4}{uv} + \frac{uv}{5}

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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. \newline4uv+uv5\frac{4}{uv} + \frac{uv}{5}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators uvuv and 55. Since uvuv and 55 have no common factors other than 11, the LCM is simply their product, which is 5uv5uv.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 55 and the second fraction by uvuv. This gives us 4×5uv×5\frac{4 \times 5}{uv \times 5} + uv×uv5×uv\frac{uv \times uv}{5 \times uv}.
  3. Perform multiplications: Perform the multiplications in the numerators and denominators. This results in 205uv+uv25uv\frac{20}{5uv} + \frac{uv^2}{5uv}.
  4. Simplify the expression: Simplify the expression by adding the numerators since the denominators are the same. The final simplified expression is (20+uv2)/(5uv)(20 + uv^2)/(5uv).

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