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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{b^3}{4} - \frac{5}{a^5}$

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Add and subtract rational expressions

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

\newline

\frac{b^3}{4} - \frac{5}{a^5}

Identify LCM: Identify the least common multiple (LCM) of the denominators $4$ and $a^5$ . Since $4$ and $a^5$ have no common factors (assuming $a$ is not a multiple of $2$ ), the LCM is simply their product, which is $4a^5$ .
Make denominators same: Make the denominators the same by multiplying the first fraction by $a^5$ and the second fraction by $4$ . This gives us $(b^3 \cdot a^5) / (4 \cdot a^5) - (5 \cdot 4) / (a^5 \cdot 4)$ .
Rewrite with common denominator: Rewrite the fractions with the common denominator. This gives us $(b^3 \cdot a^5) / (4a^5) - (20) / (4a^5)$ .
Combine numerators: Combine the numerators over the common denominator. The final simplified expression is $(b^3 \cdot a^5 - 20) / (4a^5)$ .

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