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Perform the operation and express your answer as a single fraction in simplest form. x+(1)/(xy^(2)) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newlinex+1xy2 x+\frac{1}{x y^{2}} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newlinex+1xy2 x+\frac{1}{x y^{2}} \newlineAnswer:
  1. Identify Common Denominator: Identify the common denominator for the two terms.\newlineSince the first term xx has an implicit denominator of 11 and the second term has a denominator of xy2xy^2, the common denominator is xy2xy^2.
  2. Express First Term: Express the first term xx with the common denominator xy2xy^2. To do this, multiply xx by (y2/y2)(y^2/y^2) to get (xy2)/(xy2)(xy^2)/(xy^2).
  3. Combine Fractions: Combine the two fractions over the common denominator.\newlineNow we have (xy2)/(xy2)+(1)/(xy2)(xy^2)/(xy^2) + (1)/(xy^2), which can be combined into a single fraction as (xy2+1)/(xy2)(xy^2 + 1)/(xy^2).
  4. Check for Simplification: Check if the fraction can be simplified further.\newlineThe numerator xy2+1xy^2 + 1 and the denominator xy2xy^2 have no common factors other than 11, so the fraction is already in its simplest form.

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