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Simplify. Express your answer as a single fraction in simplest form. \newline4s2+5\frac{4}{s^2} + 5

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline4s2+5\frac{4}{s^2} + 5
  1. Identify Given Expression and Goal: Identify the given expression and the goal.\newlineWe have the expression 4s2+5\frac{4}{s^2} + 5. Our goal is to combine this into a single fraction in simplest form.
  2. Find Common Denominator: Find a common denominator for the two terms.\newlineSince 55 can be written as 51\frac{5}{1}, we need to find a common denominator for 11 and s2s^2. The common denominator is s2s^2.
  3. Express 55 as Fraction: Express 55 as a fraction with the common denominator s2s^2. To do this, we multiply both the numerator and the denominator of 51\frac{5}{1} by s2s^2, which gives us 5s2s2\frac{5s^2}{s^2}.
  4. Rewrite with Common Denominator: Rewrite the original expression with the common denominator.\newlineNow we have 4s2+5s2s2\frac{4}{s^2} + \frac{5s^2}{s^2}. Since they have the same denominator, we can combine them into a single fraction.
  5. Combine Numerators: Combine the numerators over the common denominator.\newlineWe add the numerators and keep the common denominator, which gives us (4+5s2)/s2(4 + 5s^2)/s^2.
  6. Check for Further Simplification: Check if the fraction can be simplified further. In this case, the numerator 4+5s24 + 5s^2 and the denominator s2s^2 do not have any common factors other than 11, so the fraction is already in simplest form.

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