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Simplify. Express your answer as a single fraction in simplest form. \newline4v3w4−3v52\frac{4}{v^3w^4} - \frac{3v^5}{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. \newline4v3w4−3v52\frac{4}{v^3w^4} - \frac{3v^5}{2}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators v3w4v^3w^4 and 22. Since v3w4v^3w^4 and 22 have no common factors, the LCM is simply their product, which is 2v3w42v^3w^4.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 22 and the second fraction by v3w4v^3w^4. This gives us 4⋅2v3w4⋅2−3v5⋅v3w42⋅v3w4\frac{4 \cdot 2}{v^3w^4 \cdot 2} - \frac{3v^5 \cdot v^3w^4}{2 \cdot v^3w^4}.
  3. Perform multiplication in numerators and denominators: Perform the multiplication in the numerators and denominators. This results in 82v3w4−3v8w42v3w4\frac{8}{2v^3w^4} - \frac{3v^8w^4}{2v^3w^4}.
  4. Simplify the expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is 8−3v8w42v3w4\frac{8 - 3v^8w^4}{2v^3w^4}.

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