Full solution

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

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\frac{5}{st^5} - \frac{1}{2s^2}

Rewrite fractions: $\frac{5}{st^5} - \frac{1}{2s^2}$ $\newline$ Rewrite both fractions with a common denominator. $\newline$ The least common multiple (LCM) of $st^5$ and $2s^2$ is $2s^2t^5$ . $\newline$ $\frac{5}{st^5} \cdot \frac{2s}{2s} - \frac{1}{2s^2} \cdot \frac{t^5}{t^5}$
Perform multiplication: $\frac{5}{st^5} \times \left(\frac{2s}{2s}\right) - \frac{1}{2s^2} \times \left(\frac{t^5}{t^5}\right)$ $\newline$ Perform the multiplication to get the common denominator. $\newline$ $\left(\frac{5 \times 2s}{st^5 \times 2s}\right) - \left(\frac{1 \times t^5}{2s^2 \times t^5}\right)$ $\newline$ $=\frac{10s}{2s^2t^5} - \frac{t^5}{2s^2t^5}$
Combine fractions: $(\frac{10s}{2s^2t^5}) - (\frac{t^5}{2s^2t^5})$ Combine the fractions over the common denominator. $(\frac{10s - t^5}{2s^2t^5})$
Simplify fraction: $(10s - t^5)/(2s^2t^5)$ $\newline$ Simplify the fraction by reducing common factors if possible. $\newline$ There are no common factors between $10s$ and $t^5$ , and the denominator $2s^2t^5$ is already in simplest form. $\newline$ So the final simplified expression is $(10s - t^5)/(2s^2t^5)$ .