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Simplify. Express your answer as a single fraction in simplest form. \newline3y5−10xy3\frac{3}{y^5} - \frac{10xy}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline3y5−10xy3\frac{3}{y^5} - \frac{10xy}{3}
  1. Rewrite with common denominator: 3y5−10xy3\frac{3}{y^5} - \frac{10xy}{3}\newlineRewrite the expression with a common denominator.\newlineTo find a common denominator, we need to multiply each fraction by a form of 11 that will give both fractions the same denominator.\newline3y5⋅33−10xy3⋅y5y5\frac{3}{y^5} \cdot \frac{3}{3} - \frac{10xy}{3} \cdot \frac{y^5}{y^5}
  2. Multiply to get common denominator: 3y5×(33)−10xy3×(y5y5)\frac{3}{y^5} \times \left(\frac{3}{3}\right) - \frac{10xy}{3} \times \left(\frac{y^5}{y^5}\right)\newlinePerform the multiplication to get the common denominator.\newline(3×3y5×3)−(10xy×y53×y5)\left(\frac{3\times 3}{y^5\times 3}\right) - \left(\frac{10xy\times y^5}{3\times y^5}\right)
  3. Simplify numerators and denominators: (3×3)/(y5×3)−(10xy×y5)/(3×y5)(3\times3)/(y^5\times3) - (10xy\times y^5)/(3\times y^5)\newlineSimplify the numerators and denominators.\newline(9)/(3y5)−(10xy6)/(3y5)(9)/(3y^5) - (10xy^6)/(3y^5)
  4. Combine fractions over common denominator: (9)/(3y5)−(10xy6)/(3y5)(9)/(3y^5) - (10xy^6)/(3y^5)\newlineCombine the fractions over the common denominator.\newline(9−10xy6)/(3y5)(9 - 10xy^6)/(3y^5)
  5. Simplify fraction: (9−10xy6)/(3y5)(9 - 10xy^6)/(3y^5)\newlineSimplify the fraction by reducing the common factor in the numerator and the denominator if possible.\newlineHowever, in this case, there is no common factor to reduce, so the fraction is already in its simplest form.

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