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Perform the operation and express your answer as a single fraction in simplest form. (4)/(5x)+(x)/(3) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline45x+x3 \frac{4}{5 x}+\frac{x}{3} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline45x+x3 \frac{4}{5 x}+\frac{x}{3} \newlineAnswer:
  1. Identify Common Denominator: Identify a common denominator for the fractions (45x)(\frac{4}{5x}) and (x3)(\frac{x}{3}).\newlineThe least common multiple (LCM) of the denominators 5x5x and 33 is 15x15x.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator of 15x15x.
    45x\frac{4}{5x} becomes 4×35x×3=1215x\frac{4 \times 3}{5x \times 3} = \frac{12}{15x}
    x3\frac{x}{3} becomes x×5x3×5x=5x215x\frac{x \times 5x}{3 \times 5x} = \frac{5x^2}{15x}
  3. Add Fractions: Add the fractions with the common denominator.\newline(1215x)+(5x215x)=(12+5x215x)(\frac{12}{15x}) + (\frac{5x^2}{15x}) = (\frac{12 + 5x^2}{15x})
  4. Simplify Numerator: Simplify the numerator if possible.\newlineThe numerator 12+5x212 + 5x^2 cannot be simplified further because there are no common factors.
  5. Final Answer: Write the final answer as a single fraction in simplest form.\newlineThe sum of the fractions is (12+5x215x)(\frac{12 + 5x^2}{15x}).

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