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Simplify. Express your answer as a single fraction in simplest form. \newline2x−x52\frac{2}{x} - \frac{x^5}{2}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline2x−x52\frac{2}{x} - \frac{x^5}{2}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators xx and 22. Since xx and 22 are not like terms and 22 is not a factor of xx, the LCM is simply 2x2x.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 22 and the second fraction by xx. This gives us (2×2)/(x×2)−(x5×x)/(2×x)(2\times 2)/(x\times 2) - (x^5\times x)/(2\times x).
  3. Perform multiplication: Perform the multiplication in the numerators and denominators. This results in 42x−x62x.\frac{4}{2x} - \frac{x^6}{2x}.
  4. Simplify the expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (4−x6)/2x(4 - x^6)/2x.

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