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Simplify. Express your answer as a single fraction in simplest form. \newliney422y5z4\frac{y^4}{2} - \frac{2}{y^5z^4}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newliney422y5z4\frac{y^4}{2} - \frac{2}{y^5z^4}
  1. Identify LCM: Identify the least common multiple (LCM) of the denominators 22 and y5z4y^5z^4. Since 22 and y5z4y^5z^4 have no common factors other than 11, the LCM is simply their product, which is 2y5z42y^5z^4.
  2. Convert fractions: Convert each fraction to have the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by y5z4y^5z^4, and multiply the numerator and denominator of the second fraction by 22. This gives us (y4y5z4)/(2y5z4)(22)/(y5z42)(y^4 \cdot y^5z^4) / (2 \cdot y^5z^4) - (2 \cdot 2) / (y^5z^4 \cdot 2).
  3. Perform multiplication: Perform the multiplication in the numerators and denominators.\newlineThe first fraction becomes (y9z4)/(2y5z4)(y^9z^4) / (2y^5z^4) and the second fraction becomes 4/(2y5z4)4 / (2y^5z^4).
  4. Combine fractions: Combine the fractions by subtracting the numerators since the denominators are the same. The combined fraction is (y9z44)/(2y5z4)(y^9z^4 - 4) / (2y^5z^4).
  5. Check for simplification: Check if the expression can be simplified further. Since there are no common factors in the numerator and denominator that can be canceled out, the expression is already in its simplest form.

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