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Simplify. Express your answer as a single fraction in simplest form. \newline7uv5+16u\frac{7uv}{5} + \frac{1}{6u}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline7uv5+16u\frac{7uv}{5} + \frac{1}{6u}
  1. Find Common Denominator: Find a common denominator for the two fractions.\newlineThe common denominator for 55 and 6u6u is 30u30u.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator.\newlineFor the first fraction, multiply both the numerator and the denominator by 6u6u to get (7uv×6u)/(5×6u)(7uv \times 6u) / (5 \times 6u).\newlineFor the second fraction, multiply both the numerator and the denominator by 55 to get (1×5)/(6u×5)(1 \times 5) / (6u \times 5).
  3. Perform Multiplications: Perform the multiplications in the numerators and denominators.\newline(7uv×6u)/(5×6u)(7uv \times 6u) / (5 \times 6u) becomes (42u2v)/(30u)(42u^2v) / (30u).\newline(1×5)/(6u×5)(1 \times 5) / (6u \times 5) becomes 5/(30u)5 / (30u).
  4. Combine Fractions: Combine the fractions over the common denominator. \newline(42u2v)/(30u)+5/(30u)(42u^2v) / (30u) + 5 / (30u) becomes (42u2v+5)/(30u)(42u^2v + 5) / (30u).
  5. Simplify Fraction: Simplify the combined fraction if possible.\newlineIn this case, the numerator and denominator do not have common factors other than 11, so the fraction is already in simplest form.

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