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

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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{s^2t}{2} - \frac{2}{s^5}

Find LCM: Find the least common multiple (LCM) of the denominators $2$ and $s^5$ . Since $2$ and $s^5$ have no common factors other than $1$ , the LCM is simply their product, which is $2s^5$ .
Make denominators same: Make the denominators the same by multiplying the first fraction by $s^5$ and the second fraction by $2$ . This gives us $(s^2t \cdot s^5)/2s^5 - (2 \cdot 2)/2s^5$ , which simplifies to $(s^7t)/2s^5 - 4/2s^5$ .
Combine fractions: Combine the fractions since the denominators are now the same. The combined fraction is $(s^7t - 4)/2s^5$ .
Check for simplification: Check if the numerator and denominator have any common factors that can be simplified. In this case, there are no common factors, so the fraction is already in its simplest form.

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