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Simplify. Express your answer as a single fraction in simplest form. \newline17u2v3+13\frac{1}{7u^2v^3} + \frac{1}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline17u2v3+13\frac{1}{7u^2v^3} + \frac{1}{3}
  1. Rewrite as common fraction: 17u2v3+13\frac{1}{7u^2v^3} + \frac{1}{3}\newlineRewrite 13\frac{1}{3} as a fraction with the same denominator as 17u2v3\frac{1}{7u^2v^3}.\newline17u2v3+13×7u2v37u2v3\frac{1}{7u^2v^3} + \frac{1}{3} \times \frac{7u^2v^3}{7u^2v^3}\newline17u2v3+7u2v33×7u2v3\frac{1}{7u^2v^3} + \frac{7u^2v^3}{3 \times 7u^2v^3}
  2. Combine fractions: 17u2v3+7u2v33×7u2v3\frac{1}{7u^2v^3} + \frac{7u^2v^3}{3 \times 7u^2v^3}\newlineCombine the fractions over a common denominator.\newline17u2v3+7u2v321u2v3\frac{1}{7u^2v^3} + \frac{7u^2v^3}{21u^2v^3}\newline17u2v3+13\frac{1}{7u^2v^3} + \frac{1}{3}\newline=1×3+7u2v321u2v3=\frac{1 \times 3 + 7u^2v^3}{21u^2v^3}
  3. Simplify numerator: =1×3+7u2v321u2v3=\frac{1 \times 3 + 7u^2v^3}{21u^2v^3}\newlineSimplify the numerator.\newline=3+7u2v321u2v3=\frac{3 + 7u^2v^3}{21u^2v^3}
  4. Check for further simplification: =3+7u2v321u2v3=\frac{3 + 7u^2v^3}{21u^2v^3}\newlineCheck if the fraction can be simplified further.\newlineSince there are no common factors between the numerator and the denominator other than 11, the fraction is already in simplest form.

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