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Simplify. Express your answer as a single fraction in simplest form.\newline5q+2qr\frac{5}{q} + \frac{2}{qr}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.\newline5q+2qr\frac{5}{q} + \frac{2}{qr}
  1. Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators qq and qrqr. Since qrqr is just qq multiplied by rr, the LCM is qrqr.
  2. Rewrite First Fraction: Rewrite the first fraction so that both fractions have the same denominator. To do this, multiply the numerator and denominator of the first fraction by rr, which gives us (5r)/(qr)(5r)/(qr).
  3. Combine Fractions: Now that both fractions have the same denominator, we can combine them. This gives us (5rqr)+(2qr)(\frac{5r}{qr}) + (\frac{2}{qr}).
  4. Add Numerators: Add the numerators of the fractions together. This results in (5r+2)/(qr)(5r + 2)/(qr).
  5. Check for Simplification: Check if the expression can be simplified further. Since there are no common factors between the numerator and the denominator other than 11, the expression is already in its simplest form.

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