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Perform the operation and express your answer as a single fraction in simplest form. (1)/(xy^(3))-xy Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline1xy3−xy \frac{1}{x y^{3}}-x y \newlineAnswer:

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline1xy3−xy \frac{1}{x y^{3}}-x y \newlineAnswer:
  1. Rewrite as single fraction: Rewrite the subtraction of the whole number xyxy from the fraction 1xy3\frac{1}{xy^3} as a single fraction.\newline1xy3−xy\frac{1}{xy^3} - xy\newlineRewrite xyxy as a fraction with the same denominator as 1xy3\frac{1}{xy^3}.\newline1xy3−xy⋅xy3xy3\frac{1}{xy^3} - \frac{xy \cdot xy^3}{xy^3}
  2. Combine fractions: Combine the fractions.\newlineNow that we have a common denominator, we can combine the numerators.\newline(1−(xy⋅xy3))/(xy3)(1 - (xy \cdot xy^3))/(xy^3)
  3. Simplify numerator: Simplify the numerator.\newlineSimplify the expression xy×xy3xy \times xy^3 by adding the exponents of yy since the bases are the same.\newline(1−x×y1+3)/(xy3)(1 - x \times y^{1+3})/(xy^3)\newline(1−x×y4)/(xy3)(1 - x \times y^4)/(xy^3)
  4. Express final answer: Express the final answer as a single fraction in simplest form. The expression is already in simplest form, as there are no common factors between the numerator and the denominator that can be cancelled out. (1−x⋅y4)/(xy3)(1 - x \cdot y^4)/(xy^3)

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