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Simplify. Express your answer as a single fraction in simplest form. \newlineb34−5a5\frac{b^3}{4} - \frac{5}{a^5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlineb34−5a5\frac{b^3}{4} - \frac{5}{a^5}
  1. Identify LCM: Identify the least common multiple (LCM) of the denominators 44 and a5a^5. Since 44 and a5a^5 have no common factors (assuming aa is not a multiple of 22), the LCM is simply their product, which is 4a54a^5.
  2. Make denominators same: Make the denominators the same by multiplying the first fraction by a5a^5 and the second fraction by 44. This gives us (b3⋅a5)/(4⋅a5)−(5⋅4)/(a5⋅4)(b^3 \cdot a^5) / (4 \cdot a^5) - (5 \cdot 4) / (a^5 \cdot 4).
  3. Rewrite with common denominator: Rewrite the fractions with the common denominator. This gives us (b3⋅a5)/(4a5)−(20)/(4a5)(b^3 \cdot a^5) / (4a^5) - (20) / (4a^5).
  4. Combine numerators: Combine the numerators over the common denominator. The final simplified expression is (b3⋅a5−20)/(4a5)(b^3 \cdot a^5 - 20) / (4a^5).

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