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Simplify. Express your answer as a single fraction in simplest form. \newline52v4−25\frac{5}{2v^4} - \frac{2}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline52v4−25\frac{5}{2v^4} - \frac{2}{5}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 2v42v^4 and 55. The LCM of 2v42v^4 and 55 is 10v410v^4, since 2v42v^4 and 55 have no common factors other than 11 and vv is a variable.
  2. Make Denominators Same: Make the denominators the same by multiplying the first fraction by 55 and the second fraction by 2v42v^4. This gives us 52v4×55−25×2v42v4\frac{5}{2v^4} \times \frac{5}{5} - \frac{2}{5} \times \frac{2v^4}{2v^4}, which simplifies to 2510v4−4v410v4\frac{25}{10v^4} - \frac{4v^4}{10v^4}.
  3. Simplify Expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (25−4v4)/10v4(25 - 4v^4)/10v^4.

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