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

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Add and subtract rational expressions

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{5}{2v^4} - \frac{2}{5}

Find LCM of Denominators: Find the least common multiple (LCM) of the denominators $2v^4$ and $5$ . The LCM of $2v^4$ and $5$ is $10v^4$ , since $2v^4$ and $5$ have no common factors other than $1$ and $v$ is a variable.
Make Denominators Same: Make the denominators the same by multiplying the first fraction by $5$ and the second fraction by $2v^4$ . This gives us $\frac{5}{2v^4} \times \frac{5}{5} - \frac{2}{5} \times \frac{2v^4}{2v^4}$ , which simplifies to $\frac{25}{10v^4} - \frac{4v^4}{10v^4}$ .
Simplify Expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is $(25 - 4v^4)/10v^4$ .

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