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Simplify. Express your answer as a single fraction in simplest form. \newline7q32r5\frac{7q}{3} - \frac{2}{r^5}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline7q32r5\frac{7q}{3} - \frac{2}{r^5}
  1. Identify Common Denominator: Identify the common denominator for the fractions.\newlineSince the fractions 7q3\frac{7q}{3} and 2r5\frac{2}{r^5} have different denominators, we need to find a common denominator to combine them into a single fraction. The common denominator will be the product of the two denominators, which is 3×r53 \times r^5.
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator.\newlineWe will multiply the numerator and denominator of the first fraction by r5r^5 to get the common denominator, and we will multiply the numerator and denominator of the second fraction by 33 to get the common denominator.\newline(7q3)(r5r5)(2r5)(33)(\frac{7q}{3}) \cdot (\frac{r^5}{r^5}) - (\frac{2}{r^5}) \cdot (\frac{3}{3})\newline= (7qr53r5)(63r5)(\frac{7qr^5}{3r^5}) - (\frac{6}{3r^5})
  3. Combine Fractions: Combine the fractions.\newlineNow that both fractions have the same denominator, we can combine them by subtracting the numerators and keeping the common denominator.\newline(7qr56)/(3r5)(7qr^5 - 6)/(3r^5)
  4. Simplify Expression: Simplify the expression, if possible.\newlineIn this case, the numerator cannot be simplified further because there are no common factors between 7qr57qr^5 and 66. Therefore, the expression is already in its simplest form.

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