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Perform the operation and express your answer as a single fraction in simplest form. (x)/(5)+(1)/(3x) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newlinex5+13x \frac{x}{5}+\frac{1}{3 x} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newlinex5+13x \frac{x}{5}+\frac{1}{3 x} \newlineAnswer:
  1. Identify Common Denominator: Identify a common denominator for the two fractions. The common denominator for 55 and 3x3x is 15x15x.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator.\newlineThe first fraction (x5)(\frac{x}{5}) becomes (3x215x)(\frac{3x^2}{15x}) because we multiply both the numerator and the denominator by 3x3x.\newlineThe second fraction (13x)(\frac{1}{3x}) becomes (515x)(\frac{5}{15x}) because we multiply both the numerator and the denominator by 55.
  3. Add Fractions: Add the two fractions with the common denominator.\newline(3x215x)+(515x)=(3x2+515x)(\frac{3x^2}{15x}) + (\frac{5}{15x}) = (\frac{3x^2 + 5}{15x})
  4. Simplify Fraction: Simplify the fraction if possible.\newlineIn this case, the numerator and the denominator do not have common factors that can be canceled, so the fraction is already in its simplest form.

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