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Perform the operation and express your answer as a single fraction in simplest form. (5)/(x)+(4x)/(5) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline5x+4x5 \frac{5}{x}+\frac{4 x}{5} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline5x+4x5 \frac{5}{x}+\frac{4 x}{5} \newlineAnswer:
  1. Identify Common Denominator: Identify a common denominator for the two fractions.\newlineThe common denominator for (5x)(\frac{5}{x}) and (4x5)(\frac{4x}{5}) is 5x5x.
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator.\newline(5)/(x)(5)/(x) becomes (5×5)/(x×5)=(25)/(5x)(5\times5)/(x\times5) = (25)/(5x)\newline(4x)/(5)(4x)/(5) becomes (4x×x)/(5×x)=(4x2)/(5x)(4x\times x)/(5\times x) = (4x^2)/(5x)
  3. Add Fractions: Add the two fractions with the common denominator.\newline(255x)+(4x25x)=(25+4x25x)(\frac{25}{5x}) + (\frac{4x^2}{5x}) = (\frac{25 + 4x^2}{5x})
  4. Simplify Numerator: Simplify the numerator if possible.\newlineThe numerator 25+4x225 + 4x^2 cannot be factored or simplified further.
  5. Final Answer: Write the final answer as a single fraction in simplest form.\newlineThe sum of the two fractions is (25+4x25x)(\frac{25 + 4x^2}{5x}).

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