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Simplify. Express your answer as a single fraction in simplest form. \newline8rs5+r\frac{8rs}{5} + r

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline8rs5+r\frac{8rs}{5} + r
  1. Common Denominator Calculation: To combine the terms into a single fraction, we need to have a common denominator. Since the second term, rr, does not have a denominator, we can think of it as r/1r/1. To combine it with the first term, 8rs/58rs/5, we need to multiply rr by 5/55/5 to get the common denominator of 55.\newlineCalculation: r×(5/5)=(5r)/5r \times (5/5) = (5r)/5
  2. Rewriting with Common Denominator: Now we rewrite the expression with the common denominator: (8rs5)+(5r5)(\frac{8rs}{5}) + (\frac{5r}{5})
  3. Adding Numerators: Next, we add the numerators while keeping the common denominator: \newlineegin{equation}\newline\frac{88rs + 55r}{55}\newlined{equation}
  4. Factoring Out Common Factor: To simplify the numerator, we factor out the common factor rr: r(8s+5)5\frac{r(8s + 5)}{5}
  5. Final Simplified Expression: The expression is now simplified and expressed as a single fraction in simplest form. There is no further simplification possible since 8s+58s + 5 does not have any common factors with 55.\newlineFinal Answer: r(8s+5)/5r(8s + 5)/5

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